Quadratic Equations MCQs here cover topics like Quadratic formula calculator, quadratic equation calculator, completing the square calculator, and quadratic functions. Quadratic Equation questions with answers and explanations. Quadratic equations mcqs pdf, Complex Numbers MCQs with solution PDF and 100 questions on quadratic equations PDF.

## Find the roots of the quadratic equation: 2×2 + 3x – 9 = 0 ?

A. -3/2, -3

B. 3/2, 3**C. 3/2, -3**D. 3, -3/2Explanation:

2×2 + 6x – 3x – 9 = 0

2x(x + 3) – 3(x + 3) = 0

(x + 3)(2x – 3) = 0

=> x = -3 or x =**3/2.**## Roots of the equation 3×2 – 12x + 10 = 0 are ?

A. real and equal

**B. irrational and unequal**C. rational and unequal

D. complex## If the roots of a quadratic equation are 20 and -7, then find the equation ?

A. x2 + 13x + 140 = 0

**B. x2 – 13x – 140 = 0**C. x2 + 13x – 140 = 0

D. x2 – 13x + 140 = 0Explanation:

Any quadratic equation is of the form

x2 – (sum of the roots)x + (product of the roots) = 0 —- (1)

where x is a real variable. As sum of the roots is 13 and product of the roots is -140, the quadratic equation with roots as 20 and -7 is:**x2 – 13x – 140 = 0.**## Sum and the product of the roots of the quadratic equation x(power 2) + 20x + 3 = 0 are ?

**A. -20, 3**B. -10, -3

C. 10, 3

D. -10, 3## If the roots of the equation 2×2 – 5x + b = 0 are in the ratio of 2:3, then find the value of b ?

A. 12

B. 43**C. 3**D. 5Let the roots of the equation 2a and 3a respectively.

2a + 3a = 5a = -(- 5/2) = 5/2 => a = 1/2

Product of the roots: 6a2 = b/2 => b = 12a2

a = 1/2, b =**3.**## Sum of the squares of two consecutive positive integers exceeds their product by 91. Find the integers ?

A. 11, 12

B. 12, 13**C. 9, 10**D. 10, 11Explanation:

Let the two consecutive positive integers be x and x + 1

x2 + (x + 1)2 – x(x + 1) = 91

x2 + x – 90 = 0

(x + 10)(x – 9) = 0 => x = -10 or 9.

As x is positive x = 9

Hence the two consecutive positive integers are 9 and 10.## One root of the quadratic equation x2 – 12x + a = 0, is thrice the other. Find the value of a ?

A. 12

B. 45**C. 27**D. 29Explanation:

Let the roots of the quadratic equation be x and 3x.

Sum of roots = -(-12) = 12

a + 3a = 4a = 12 => a = 3

Product of the roots = 3a2 = 3(3)2 =**27.**## Sm of the square of the three consecutive even natural numbers is 1460. Find the numbers ?

A. 22, 24, 26

B. 24, 26, 28**C. 20, 22, 24**D. 18, 20, 22Explanation:

Three consecutive even natural numbers be 2x – 2, 2x and 2x + 2.

(2x – 2)2 + (2x)2 + (2x + 2)2 = 1460

4×2 – 8x + 4 + 4×2 + 8x + 4 = 1460

12×2 = 1452 => x2 = 121 => x = ± 11

As the numbers are positive, 2x > 0. Hence x > 0. Hence x = 11.

Required numbers are**20, 22, 24.**## If a and b are the roots of the equation x2 – 9x + 20 = 0, find the value of a2 + b2 + ab ?

**A. 61**B. 65

C. -21

D. 1Explanation:

a

^{2}+ b^{2}+ ab = a^{2}+ b^{2}+ 2ab – ab

i.e., (a + b)^{2}– ab

from x^{2}– 9x + 20 = 0, we have

a + b = 9 and ab = 20. Hence the value of required expression (9)^{2}– 20 =**61.**## Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 8x + 4 = 0 ?

**A. 14**B. 3

C. 24

D. 21Explanation:

a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab

= [(a + b)2 – 2ab]/ab

a + b = -8/1 = -8

ab = 4/1 = 4

Hence a/b + b/a = [(-8)2 – 2(4)]/4 = 56/4 =**14.**