Quadritic Equation

1

Quadratic Equations (Q.1) If p and q are the roots of ax2 – 5x + c = 0 such that p + q = pq = 10, then the respective values of a and c are (A) (1, 10).(B) (1/10, 1/5).(C) (1/2, 1/5).(D) (1/2, 5). (Q.2) The perimeter of a rectangular room is 34 m and the length of a diagonal is 13 m. The dimensions of the room are

(1 Mark) (1 Mark)

(A) 9 m & 2m(B) 15 m & 2m(C) 12 m & 5m (D) 17 m & 7m (1 Mark) (Q.3) Find the value of k, if the expression x2 + kx + 1 is factorizable into two linear factors. (A) (B) (C) Either or (D) Neither or (1 Mark) (Q.4) For a quadratic equation, is one root. The other root must be (A) (B) (C) 3 (D) 5 (Q.5) If the sum of the roots of the quadratic equation 3x2 + (2k +1)x – (k + 5) = 0 is equal to the product of the roots, (1 Mark) then the value of ‘k’ is

(A) 4(B) -4(C) 1 (D) -1 (Q.6) If one of roots of x2 + ax + 4 = 0 is twice the other root, then the value of ‘a’ is (A) (B) 2 (C) (D) (Q.7) If a and b are the roots of the quadratic equation x2 + px +12 = 0 with the condition a – b = 1, then the value of

(1 Mark) (1 Mark)

‘p’ is

(A) 1 (B) 7 or 1(C) –7(D) 7 or –7 (1 Mark) has (Q.8) The equation (A) no roots (B) two real roots(C) Infinitely many roots (D) three roots (Q.9) The number of roots satisfying the equation is/are (A) 1(B) 2(C) 3(D) 4 then 4x equals (Q.10) If (A) 0(B) 1 (C) (D) 5 (Q.11) The sum of the reciprocals of the roots of the equation x2 + px + q = 0 is

(A)

(B)

(C)

(1 Mark) (1 Mark) (1 Mark)

(D)

(Q.12) The discriminant of with a, c and real constants is zero. The roots must be (A) equal and integral (B) rational and equal(C) real and equal (D) imaginary (Q.13) The roots of the equation ax2 + bx + c = 0 will be reciprocal if (A) a = b (B) a = b = c(C) b = c(D) c = a

(1 Mark)

(Q.14) The roots of the equation are (A) real and equal (B) rational and equal(C) rational and unequal (D) Imaginary (Q.15) If one root of the equation a(b – c)x2 + b(c – a)x + c(a – b) = 0 is 1, then the other root is

(1 Mark)

(A)

(B)

(C)

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(1 Mark)

(D) (1 Mark)

(Q.16) In the equation

the roots are equal when

(1 Mark) (A)

(B)

(C) m = 1(D) m = 3

(Q.17) The equation has (A) two real roots and one imaginary root (B) one real and one(C) two imaginary roots (D) one real root (1 Mark) (Q.18) The least value of ax2 + bx + c (a > 0) is (A) (B) (C) (D) cannot be determined (Q.19) The product of two consecutive odd numbers is 143. The numbers are (A) 11 & 13 (B) 13 & 15(C) –11 & 13 (D) –11 & 15 (Q.20) If a = b = c, then the roots of the equation (x – a)(x – b) + (x – b)(x – c) + (x – c)(x – a) = 0 are (A) real and unequal (B) imaginary(C) real and equal (D) None of these (Q.21) If the roots of the equation (a – b)2 + (b – c)x + (c – a) = 0 are equal. Then (A) 2b = a + c (B) 2a = b + c(C) 2c = a + b (D) a = b + c (Q.22) The coefficient of x in the quadratic equation x2 + px + q = 0 was taken as 17 in the place of 13 and its roots were found to be –2 and –15. The roots of the original equation are (A) –3 or 10 (B) –3 or –10(C) 3 or –10(D) None of these

(1 Mark) (1 Mark)

(1 Mark) (1 Mark)

2 (Q.23) If a & b are the roots of x2 – px + q = 0, then a2 + b2 = is (A) p2 + q2(B) p2 + 2q(C) p2 – q2 (D) p2 – 2q (Q.24) The values of ‘k’ for which the equation 2x2 – kx + x + 8 = 0 will have real and equal roots are (A) 9 and –7 (B) only 9(C) only –7 (D) –9 and 7 (Q.25) The roots of (x2 – 3x + 2)(x)(x – 4) = 0 are (A) 1, 3 and 4(B) 0 and 4(C) 0, 1, 2 and 4 (D) 1, 2 and 4 (Q.26) The difference of the roots of x2 – 7x – 9 = 0 is (A) 7 (B) –9(C) (D) (Q.27)

(1 Mark) (1 Mark)


(A) 0.(B) k.(C) a2.(D) b2. (Q.28) If the sum of the squares of the roots of the equation x2 + 2x – p = 0 is 8, then the (1 Mark) value of p will be (A) -6.(B) -2.(C) 2.(D) 6. (Q.29) If one root of the quadratic equation x2 + bx + c = 0 is square of the other, then b3 + c2 + c equals (A) bc.(B) 2bc.(C) 3bc.(D) 6bc.

(1 Mark)

(Q.30) The set of values of k, for which x2 + 5kx + 16 = 0 has no real root, is

Top (1 Mark)

(A) (B) (C) (D) -8 < k < 8. (Q.31) If p and q are the roots of the equation x2 + px + q = 0, then (A) p = -1.(B) p = 1 or 0.(C) p = -2.(D) p = -2 or 0. (Q.32) If the equation 4x2 + x(p+1) + 1 = 0 has exactly two equal roots, then one of the

(1 Mark) (1 Mark)

values of p is

(A) 5.(B) 3.(C) 0.(D) -3. (Q.33) The condition according to which one root of the equation ax2 + bx + c = 0 is three (1 Mark) times the other is (A) b2 = 8ac. (B) 3b2 = 5ac.(C) 3b2 = 16ac.(D) b2 + 3ac = 0. (Q.34) The roots of the equation (x + 3)(x – 3) = 25 are (A) 8 and 2.(B) 5 and -5.(C) 3 and -3.(D) 34 and - 34.

(Q.35) If (X-3)- (X+3)-3=0 then 4x equals (A) 13 (B) (C) 1(D) 0 (Q.36) A dealer sells a toy for Rs 24 and gains as much percent as the cost price of the toy. Find the cost price of the toy. (A) Rs 10(B) Rs 15(C) Rs 20(D) Rs 25 (Q.37) If one root of x2 – x –m = 0 is square of the other, then m = (A) 2 ± 3.(B) 3 ± 2.(C) 2 ± 5.(D) 5 ± 2. (Q.38) The number of roots satisfying the equation is/are (A) 1(B) 2(C) 3(D) Unlimited (Q.39) If the roots of the quadratic equation x2 – px + q = 0 differ by unity, then (A) p2 = 4q + 1.(B) p2 = 4q – 1.(C) p2 = 4p + 1.(D) p2 = 4p – 1. (Q.40) The product of the roots of the equation ax – ax2 = 1 is (A) 1.(B) a.(C) 1/a.(D) 1/a2. (Q.41) The product of two consecutive positive integers is 240. Formulate the quadratic equation whose roots are these integers. (A) x2 + x – 120(B) x2 + x – 240(C) x2 – x – 240(D) x2 (Q.42) Find the zeroes of the polynomials x2- 3. (A)

(B)

(C)

(B)

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(1 Mark) (1 Mark) (1 Mark) (1 Mark) (1 Mark)

(1 Mark)

(D) (1 Mark)

(Q.43) Solve the equation : (A)

(1 Mark)

(C) -2,-3(D) -4,-3 (1 Mark)

(Q.44) The sum of two numbers is 15. If the sum of their reciprocal is , find the two numbers. (A) 1, 5(B) 8,7(C) 15, 10(D) 10, 5 (Q.45) One side of a right triangle exceeds the other side by four inches. The hypotenuse is 20 inches. The length of the shorter side of the right triangle will be (A) 8 inches.(B) 12 inches.(C) 16 inches.(D) 18 inches.

(Q.46)

Top (1 Mark) (1 Mark)

3 (A) (2, 1).(B) (-1, 3).(C) (-1, 1).(D) (1, -3). (1 Mark) (Q.47) (A) 1/9.(B) 16/9.(C) 7/3.(D) 49/9. (Q.48) The sum of the two solutions of the quadratic equation x2 – 6x + 5 = 0 is (A) -6.(B) -5.(C) 5.(D) 6.

(1 Mark) (1 Mark)

(Q.49) Meena solved a quadratic equation and found the solutions to be The quadratic equation that was solved by Meena is (A) (x - 6)(3x + 2) = 0.(B) (x - 6)(2x + 3) = 0.(C) (x + 6)(2x - 3) = 0.(D) (x + 6)(3x - 2) = 0. (Q.50) The value(s) of x that makes the quadratic equation x2 – 16 = 0 as true is/are (A) x = 4.(B) x = -8.(C) x = 4 or x = -4.(D) x = 8 or x = -8. (Q.51) The solutions of the quadratic equation x2 + 2x – 3 = 0 are (A) x = 1 or x = 3.(B) x = -1, or x = 3.(C) x = 1 or x = -3.(D) x = -1 or x = -3. (Q.52) If the price of an article is increased by Rs 2 per dozen than the present price, the


number of things available for Rs 56 is 8 less than before. The prize per dozen at present is (A) Rs 10.(B) Rs 12.(C) Rs 14.(D) Rs 18. (Q.53) If a, b are the roots of the equation x2 + px + q = 0 and a4, b4 are the roots of x2 – (1 Mark) rx + s = 0, then the equation x2 – 4qx + 2q2 – r = 0 has always (p, q, r, s are real numbers) (A) two real roots. (B) two negative roots.(C) two positive roots.(D) one positive and one negative root. (1 Mark) (Q.54) If sin a and cos a are the roots of the equation px2 + qx + r = 0, then 2 2 2 2 2 2 2 2 2 2 (A) p – q + 2pr = 0.(B) (p + r) = q – r .(C) p + q – 2pr = 0.(D) (p – r) = q + r . (1 Mark) (Q.55) If f(x) = ax2 + bx + c, g(x) = - ax2 + bx + c where ac 0, then f(x) g(x) = 0 has (A) at least three real roots.(B) no real roots.(C) at least two real roots. (D) two real roots and two imaginary roots. (Q.56) If one root of the equation 8x2 – 6x – a - 3 = 0 is the square of the other, then the (1 Mark) values of a are (A) 4, -24.(B) 4, 24.(C) -4, -24.(D) -4, 24. (1 Mark) 2 (Q.57) If ax + bx + c = 0 is satisfied by every value of x, then (A) b, c = 0.(B) c = 0.(C) a = 0.(D) a = b = c = 0. (1 Mark) (Q.58) If c and d are the roots of the equation (x – a) (x –b) – k = 0, then a, b are the roots of the equation (A) (x – c) (x – d) – k = 0.(B) (x – c) (x – d) + k = 0.(C) (x – a) (x – c) + k = 0.(D) (x – b) (x – d) + k = 0. (Q.59) If a, b are the roots of x2 – 3x + 2 = 0, then the equation with roots (a + 1), (b+1) (1 Mark) is (A) x2 – 5x – 6 = 0.(B) x2 + 5x – 6 = 0.(C) x2 + 5x + 6 = 0.(D) x2 – 5x + 6 = 0.

(Q.60) The solution of the equation (A) 3, 4.(B) 5, 1.(C) -3, 4.(D) 4, -3. (Q.61) Rahul and Sameer solved a quadratic equation. While solving it, Rahul made a mistake in the constant term and obtained the roots as 5, -3, whereas Sameer made a mistake in the coefficient of x and obtained the roots as 1, -3. The correct roots of the quadratic equation are (A) 1, 3.(B) -1, 3.(C) -1, -3.(D) 1, -1. (Q.62) The highest integral value of ‘m’ for which the quadratic equation x2 – 6x + m = 0 have two real and distinct roots is

(A) 9.(B) 8.(C) 7.(D) 3. (Q.63) The solution of x2 – 3x – 40 = 0 will be (A) -5 and -8.(B) 5 and -8.(C) -5 and 8.(D) 5 and 8. (Q.64) If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then the value of m is (A) –22.5.(B) -17.5.(C) -10.5.(D) 16. (Q.65) If (x – 3)(2x + 1) = 0, then possible value(s) of 2x + 1 will be (A) 0 only.(B) 0 and 3.(C) – ½ and 3.(D) 0 or 7. (Q.66) If the roots of ax2 + bx + c = 0 are equal, then the value of c is (A) –b/2a.(B) b/2a.(C) –b2/4a.(D) b2/4a. (Q.67) If the quadratic equation 2x2 + 3x + p = 0 has equal roots, then the value of p will be (A) 4/3.(B) 5/4.(C) 6/5.(D) 9/8. (Q.68) The roots of the equation x2 - 3x - 18 = 0 are (A) {6, 3}.(B) {6, -3}.(C) {-6, 3}.(D) {-6, -3}. (Q.69) The quadratic equation whose roots are reciprocal of the roots of the equation ax2 + bx + c = 0 is (A) cx2 + bx + a = 0.(B) bx2 + cx + a = 0.(C) cx2 + ax + b = 0.(D) bx2 + ax + c = 0.

Top (1 Mark) (1 Mark)

(1 Mark) (1 Mark) (1 Mark) (1 Mark) (1 Mark) (1 Mark) (1 Mark) (1 Mark)

4 (Q.70) If the equations x2 +ax + b = 0 and x2 +bx + a = 0 have a common root, then the

(1 Mark)

numerical value of a + b is (A) 2.(B) 1.(C) 0.(D) -1. (Q.71) If a, b, c are positive real numbers, then the roots of the equation ax2 + bx + c = 0 (1 Mark) (A) are real and positive.(B) are real and negative.(C) have negative real part.(D) have positive real part. (1 Mark) (Q.72) If p and q are the roots of the quadratic equation x2 + mx + m2 + a = 0, then the value of p2 + q2 + pq is (A) 0.(B) a.(C) –a.(D) ± m2. (1 Mark) 2 (Q.73) The condition according to which one root of the equation ax + bx + c = 0 may be double of the other is (A) 2b2 = 9ac.(B) 2b2 = ac.(C) b2 = 9ac.(D) b2 = ac. (1 Mark) (Q.74) The roots of the quadratic equation 5x2 + 19x = 4 are (A) {-1/5, -4}.(B) {1/5, -4}.(C) {-1/5, 4}.(D) {1/5, 4}. (1 Mark) (Q.75) If both roots of the equation ax2 + bx + c = 0 are zero, then (A) b = 0, c = 0.(B) b = 0, c ≠ 0.(C) b ≠ 0, c = 0.(D) b ≠ 0, c ≠ 0. (1 Mark) (Q.76) If the ratio of the roots of x2 +px + c = 0 and x2 +qx + r = 0 are same, then (A) r2c = p2q.(B) r2p = c2q.(C) rp2 = cq2.(D) rc2 = pq2. (Q.77) If the difference between the roots of the equation x2 + px + 8 is 2, then the value (1 Mark) of p is (A) ±2.(B) ±4.(C) ±6.(D) ±8. (1 Mark) (Q.78) If one root of the equation 6x2 + 13x + m = 0 is reciprocal of the other, then the value of m is (A) 1/7.(B) 1/6.(C) 6.(D) 7. (Q.79) If the roots of a quadratic equation are rational and unequal, then the discriminant (1 Mark) is (A) zero.(B) negative.(C) a perfect square.(D) not a perfect square.

(Q.80) The number of terms in the standard form of a quadratic equation is (A) 1.(B) 2.(C) 3.(D) 4. (Q.81) If a and b are the roots of the equation x2 - 6x + 6 = 0, then the value of a2 + b2 is (A) 36.(B) 24.(C) 12.(D) 6. (Q.82) If x = 2 and x = 3 are roots of equation 3x2 – 2kx + 2m = 0, find the value of k and m. (A) (B) (C) 14, 3(D) (Q.83) Solve the quadratic equation by factorization method: (A) +3(B) 3,3(C) 3,0(D) 0,3

x2 – 9 = 0

(Q.84) Solve 20071204453718001196751909 _image022.wmz" o:title=""/> (A) 1,0(B) 0,1(C) 1,-1(D) -1,-1 (Q.85) Solve the quadratic equation : 15x2 – 28 = x (A) 1, -2(B) -2, 5(C) (D) (Q.86) Find the discriminant of the quadratic equation:3x2 – 5x – 2 = 0 (A) 49(B) 50(C) 51(D) 52 (Q.87) For what value of p, the given equation has real roots? 2x2 + 2x + p = 0 (A) (B) 2 p(C) (D) 1 p (Q.88) Find the value of ‘k’ so that the equation 9x2 – kx + 81 = 0 has equal roots (A) +50, -50(B) +52, -52(C) +54,-54(D) +56, -56 (Q.89) If -4 is a root of the quadratic equation x2 + px – 4 = 0, find the value of p. (A) 3(B) 4(C) 5(D) 6 (Q.90) What is the nature of the roots of the quadratic equation: 3x2 – 5x + 2 = 0 (A) Real(B) Unequal(C) Real and unequal(D) Equal (Q.91) Find the sum and product of zeroes of the polynomials: x2 + 7x + 10. (A) 7, 10(B) -7, 10(C) -7,-10(D) -10,-12 (Q.92) Find the sum and product of zeroes of cubic polynomials p(x) = 3x3 – 5x2 – 11x – 3



(1 Mark) (1 Mark)

(1 Mark) (1 Mark) (1 Mark) (1 Mark) (1 Mark) (1 Mark)

(A) (B) (C) (D) (Q.93) The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides. (A) -12.0 cm , -5.0 cm (B) -12 cm , 5.0 cm (C) 12.0 cm , 5.0 cm (D) 8.0 cm, 1.0 cm (Q.94) Rohan’s mother is 26 years older than he. The product of their ages, 3 years from now will (1 Mark) be 360. (A) x2+ 32x - 273 = 0(B) x2 + 30x - 275 = 0(C) x2 + 33x - 270 = 0(D) x2 + 32x - 263 = 0

5 (1Mar k)

(Q.95) Using quadratic formula, solve the following quadratic equation for x : (A) a + b, a – b(B) a +2b, a – 2b(C) 2a + b, 2a – b(D) 2a+2b ,2a-2b (Q.96) The equation has (A) Two real roots and one imaginary root(B) One real and one imaginary root(C) Two imaginary roots (D) One real root (Q.97) The difference of the roots of x2 – 5x – 7 = 0 is (A) (B) (C) 5 (D) -7 (Q.98) If one root of the equation p(q – r)x2 + q(r – p)x + r(p – q) = 0 is 1, then the other root is (A) (B) (C) (D) (Q.99) If the roots of the equation 12x2 + mx + 5 = 0 are in the ratio 3 : 2, then the

(1 Mark)

(1 Mark) (1 Mark)

(1 Mark)

value(s) of m is (A) -6√5. (B) 6√5.(C) ±5√10.(D) ±6√10.

(Q.100) The difference of two numbers is 5 and the difference of their reciprocal is 1/10. Find the numbers. (Q.101) By increasing the list price of a book by Rs. 10 a person can buy 10 books less for Rs. 1,200. Find the original list price of the book. (Q.102) The hypotenuse of a right angled triangle is 6cm more than twice the shortest side. If the third side is 2cm less than the hypotenuse, find the side of the triangle. (Q.103) A passenger train takes 2 hr less for a journey of 300 km. if its speed increased by 5km/hr from its usual speed. Find its usual speed. (Q.104) The numerator of a fraction is one less than its denominator. If three is added to each the numerator and denominator, the fraction is increased by 3/28. Find the fraction.

(5Marks) [CBSE-DELHI 2007]




(5Marks) [CBSE-Outside Delhi 2007]

(5Marks) (Q.105) The difference of square of two natural numbers is 45. The square of the smaller number is [CBSEOutside Delhi four times the larger number. Find the numbers. 2007]

(Q.106) A train travels a distance of 300 km at a uniform speed. If the speed of the train is increased (4arks) [CBSE-DELHI 2006] by 5km an hour, the journey would have taken two hours less. Find the original speed of the train. (3Marks) (Q.107) Using the quadratic formula, solve the equation: a2b2x2 – (4b4 – 3a4)x – 12a2b2 = 0 [CBSE-Outside Delhi 2006]

(Q.108) The sum of two natural numbers is 8. Determine the numbers if the sum of their reciprocals is 8/15.

(3Marks) [ CBSE-Outside Delhi

2006]

(Q.109) The speed of a boat in still water is 11 km/hr. It can go 12 km upstream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream.



(Q.110) Solve for x.

(3Marks)

(Q.111) Solve for x.

[CBSE-DELHI 2005]

(4Marks) (Q.112) The sum of two numbers is 16. The sum of their reciprocals is.

Find the numbers.

[CBSE-DELHI 2005]

(Q.113) The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.

(4Marks)

(Q.114) The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.

(4Marks)

(Q.115) A two digit number is four times the sum of its digits and twice the product of the

(3Marks)

digits. Find the number.

[CBSE-Outside Delhi 2005]

(Q.116) Solve for x:

[CBSE-DELHI 2006]

[CBSE-DELHI 2005]

(3arks) [CBSE-Outside Delhi 2005]


(Q.117) Solve for x: (Q.118) A two digit number is such that the product of its digits is 15. If 18 is added to the


number, the digits interchange their places, find the number. (Q.119) A two digit number is such that the product of its digits is 20. If 9 is added to the number, the digits interchange(4Marks) their places. Find the number. [CBSE-Outside Delhi 2005]

(Q.120) Solve for x: 4x2 - 2(a2 + b2)x + a2b2 = 0



(Q.121) Solve for (Q.122) A farmer wishes to grow a 100 m2 rectangular vegetable garden. Since he has with (6Marks) him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side-fence. Find the dimensions of his garden.

[CBSE-DELHI 2003]

6 (Q.123) The distance between Mumbai and Pune is 192 km. Travelling by Deccan Queen, it takes 48 minutes less than another train. Calculate the speed of the Deccan Queen, if the speed of the two trains differ by 20 km/hr. (Q.124) Determine value(s) of p for which the quadratic equation 4x2 - 3px + 9 = 0 has real roots. (Q.125) 300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.



(4 arks) [CBSE-Outside Delhi 2004]


(Q.126) Solve for (Q.127) Using quadratic formula, solve the following quadratic equation for x. p2x2 + (p2 - q2)x - q2 = 0 (Q.128) In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 marks more in mathematics and 4 marks less in science, the product of marks obtained in two subjects would have been 180. Find the marks obtained in the two subjects separately. (Q.129) The sum of the areas of two squares is 640 m2. If the difference in their perimeters be 64 m, find the sides of the two squares.



(6 arks) [CBSE-DELHI 2008]


(Q.130) Find the roots of the following equation:


(Q.131)

(3Marks)

Q.132) Solve for x: 4x2 - 4a2x + (a4 - b4) = 0

[CBSE-DELHI

2004] (Q.133) A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km 6 Marks)

upstream than to return downstream to the same spot. Find the speed of the stream. (Q.134) Find the roots of the quadratic equation (x+6)2 = 64. (Q.135) Product of two consecutive positive integers is 240. Find the integers. (Q.136) The area of a right angled triangle is 600 cm2. If the base of the triangle exceeds the altitude by 10 cm, find the dimensions of the triangle. (Q.137) If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then find the value of m.

[CBSE-Outside Delhi 2008]

(2 arks) (1 Mark) (6Marks) 3 Marks) 6 Marks)

(Q.138) Two pipes running together can fill a cistern in

minutes. If one pipe takes 3 minutes more than the other to fill it, find the time taken by each pipe to fill the cistern. (Q.139) Seven years ago Varun’s age was five times the square of Swati’s age. Three years hence Swati's age will be two 6 fifth of Varun’s age. Find their present ages.

Marks)

Most Important Questions (Q.140) A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed. (Q.141) In the sum of n successive odd natural numbers starting from 3 is 48, find the value of n. (Q.142) Divide 16 into two positive numbers such that twice the square of the larger part exceeds the square of the

6 Marks) 3 Marks) 3 Marks)

smaller part by 164.

(Q.143) If –4 is a root of the quadratic equation equal roots, find the value of

and the quadratic equation

has

3 Marks)

.

(3Marks) (Q.144) If the equation 4x2 + x(p+1) + 1 = 0 has exactly two equal roots, then find the values of p. (Q.145) A two digit number is such that the product of its digit is 18. When 63 is subtracted from the number, the digits (3Marks) interchange their places. Find the number. (Q.146) Find the values of k for which the given equation has equal roots.

(Q.147) Using quadratic formula solve the equation for

(2Marks) (2Marks)

. ,

(Q.148) Solve by factorization method.

(2arks) (2Marks)

(Q.149) Solve the quadratic equation by factorization method. (Q.150) (Q.151) (Q.152) (Q.153)

If one root of the quadratic equation is 2, find the value of . Also find the other root. If the sum of the squares of the roots of the equation x2 + 2x – p = 0 is 8, find the value of p. The product of two successive multiples of 5 is 300. Determine the multiples. If one root of the equation 6x2 + 13x+ m = 0 is reciprocal of the other, find the value of m.

(2Marks) (1Mark) (2 arks) (1Mark)

7 (2arks) (Q.154) (Q.155) Solve the equation x2 - 9 = 0. (Q.156) Find the roots of the equation x2 - 3x - 18 = 0. (Q.1) Check whether the following are quadratic equations: (i)

(1Mark) (1Mark) (ii)

(iii)

(Q.2) Solve (x + 7)(x – 3) = 0 (Q.3) Solve (Q.4) Solve (Q.5) Solve (Q.6) Solve (Q.7) Solve by the method of completing the square

(Q.8) Solve (Q.9) Solve

by the method of completing the square

(Q.10) Find the roots of

by quadratic formula

(Q.11) Find the nature of the roots of quadratic equation (Q.12) Find the values of k for which the quadratic equation

has real and distinct roots.

(Q.13) Find the values of k for which the quadratic equation has real and equal roots. (Q.14) Find two successive even natural numbers whose squares have the sum 452. (Q.15) The sum of two numbers is 12. If the sum of their reciprocal is , Find the two numbers. (Q.16) A two-digit number is such that the product of the digits is 18. When 27 is reduced from this number the digits interchange their places. Determine the number.

(Q.17) If the length of a rectangle is 17 cm more than the breadth and its area is 168 sq.cm, find its dimensions. (Q.18) A local train travels a distance of 450km at uniform speed. Due to some problem, speed had been 15 km/hr less. Train took 1 hour 30 minutes more to cover the same distance. Find the speed of the local train. (Q.19) The difference of the squares of two numbers is 45. The Square of the smaller number is 4 times the larger number. Determine the numbers . (Q.20) The sum of the first even natural numbers is 420, Find the value of n.

Quadritic Equation

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