Mastering Quadratic Equations for CAT: Your Ultimate Practice Guide 1
- Aug 8
- 5 min read
Welcome to a new chapter in your CAT Quantitative Aptitude preparation! While linear equations lay the groundwork, quadratic equations introduce a new layer of complexity and are a frequent fixture in the CAT exam. A solid understanding of their concepts, formulas, and solving techniques is essential for securing a high score. Boost your CAT score with our comprehensive guide to quadratic equations. This blog post breaks down core concepts and provides a detailed practice sheet with solutions to help you master this essential Quantitative Aptitude topic for the exam.
Practicse Sheet 1
Q.1 Find the sum and product of roots of given quadratic equation: -2x2 - 7x + 12 = 0.
Hint: Please note that the coefficient of x2 here is -2 and not 2.
a.7/2, - 12
b.-7/2, 12
c.-7/2, -6
d.7/2, -6
Q.2 If one root of -3x2 + 12x + k = 0 is the reciprocal of the other root, then find value of k.
a.1
b.-1
c.3
d.-3
Q.3 If the roots of quadratic equation x2 - kx + 9 = 0 are equal, then find the value of k.
a.6
b.-6
c.Both (a) and (b)
d.None of these
Q.4 Find the quadratic equations whose roots are the reciprocals of the roots of x2 + 6x - 5 = 0.
a.5x2 - 6x + 1 = 0
b.5x2 + 6x + 1 = 0
c.5x2 + 6x - 1 = 0
d.5x2 - 6x - 1 = 0
Q.5 If roots of quadratic equation ax2 + bx + c = 0 are α and β, then find the quadratic equation whose roots are 2α and 2β.
a.ax2 + 2bx - 4c = 0
b.ax2 - 2bx - 4c = 0
c.ax2 - 2bx + 4c = 0
d.ax2 + 2bx + 4c = 0
Q.6 If one roots of quadratic equation is (3 + √5), then find the quadratic equation.
a.x2 + (3 + √5)x + 6 = 0
b.x2 + (3 - √5) x + 4 = 0
c.x2 - 6x + 4 = 0
d.x2 + 6x - 4 = 0
Q.7 If roots of quadratic equation 2x2 - 5x - 12 = 0 are α and β, then find the quadratic equation whose roots are (α - 2) and (β - 2).
a.x2 - 3x + 14 = 0
b.x2 + 3x - 14 = 0
c.2x2 + 3x - 14 = 0
d.2x2 - 3x + 14 = 0
Q.8 If roots of quadratic equation x2 - 8x + 25 = 0 are α and β, then find the quadratic equation whose roots are α2 and β2.
a.x2 - 16x + 125 = 0
b.x2 - 16x + 625 = 0
c.x2 - 14x + 125 = 0
d.x2 - 14x + 625 = 0
Q.9 If roots of quadratic equation x2 + 3x - 10 = 0 are α and β, then find the quadratic equation whose roots are α3 and β3.
a.x2 - 117x - 1000 = 0
b.x2 + 117x - 1000 = 0
c.x2 - 117x + 1000 = 0
d.None of these
Q.10 If roots of quadratic equation x2 - 5x + 5 = 0 are α and β, then find the quadratic equation whose roots are (α2 + 2) and (β2 + 2).
a.x2 - 15x + 55 = 0
b.x2 - 19x + 55 = 0
c.x2 - 15x + 59 = 0
d.x2 - 19x + 59 = 0
Q.11 If α, β are the roots of the equation ax2 + bx + c = 0, then what is the quadratic equation whose roots are (2α + 3β) and (3α + 2β)?
a.a2x2 + 5abx + 6b2 + ac = 0
b.a2x2 - 5bx + 6b2 - ca = 0
c.a2x2 - 5bx - 6b2 + ca = 0
d.Cannot be determined
Q.12 What can be the value of k, for which roots of the equation x2 - 6x + k = 0 are real and distinct?
a.8
b.9
c.10
d.11
Q.13 If roots of quadratic equation x2 - 6x + 10 = 0 are α and β, then find the quadratic equation whose roots are (α/β) and (β/α).
a.x2 - 8x + 1 = 0
b.x2 - 8x + 5 = 0
c.5x2 - 8x + 5 = 0
d.None of these
Q.14 If α and β are the roots of the quadratic equation x2 + 3x - 6 = 0. Then, find the quadratic equation whose roots are (α + 1/α) and (β +1/β).
a.6x2 + 15x - 58 = 0
b.6x2 - 15x + 58 = 0
c.3x2 + 15x - 29 = 0
d.3x2 - 15x + 29 = 0
Q.15 In the quadratic equation ax2 - bx + c = 0, if the given equation has equal roots and the product of both roots is 4, then, what is the ratio of b:c?
a.1 : 1
b.1 : 2
c.2 : 1
d.2 : 3
Q.16 If α and β are roots of the equation 5x2 - 15x + 10 = 0, then find the value of (α2 + β2).
a.3
b.4
c.5
d.6
Q.17 The roots of the equation x2 + px + q = 0 are 1 and 2. The roots of the equation qx2 - px + 1 = 0 must be:
a.1, 1/2
b.-1, -1/2
c.1, -1/2
d.-1, 1/2
Q.18 If α and β are roots of the equation 5x2 - 15x + 10 = 0, then find the value of (α3 + β3).
a.9
b.12
c.15
d.18
Q.19 If the roots of px2 + qx + 2= 0 are reciprocal to each other, then
a.P = 0
b.P = 1
c.P = 2
d.P = -2
Q.20 α and β are the roots of the equation x2 + 2x - 15 = 0, then find the quadratic equation whose roots are (α + 2) and (β + 2).
a.x2 + 2x + 15 = 0
b.x2 - 2x - 15 = 0
c.x2 - 2x + 15 = 0
d.cannot be determined
Q.21 If p and q are the roots of the equation 2x2-7x+6=0, then (1+p)(1+q) will be
a.16/2
b.15/2
c.17/2
d.18/2
Q.22 α and β are the roots of the equation x2 + 2x - 15 = 0, then find the quadratic equation whose roots are (3α) and (3β).
a.x2 + 4x - 30 = 0
b.x2 - 6x - 45 = 0
c.x2 - 6x + 135 = 0
d.x2 + 6x - 135 = 0
Q.23 The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b2 + c?
a.3721
b.549
c.361
d.427
Q.24 If ax2 + bx + c = 0 has root α and β then which of the following will be one of the quadratic equations whose roots are 1/α and 1/β?
a.ax2 + bx + c = 0
b.bx2 + ax + c = 0
c.cx2 + ax + b = 0
d.cx2 + bx + a = 0
ANSWERS
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
C | D | C | D | D | C | C | D | B | D |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
A | A | C | A | A | C | B | A | C | B |
21 | 22 | 23 | 24 | ||||||
B | D | B | D |
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