Mastering Quadratic Equations for CAT: Your Ultimate Practice Guide 2
- Aug 8
- 4 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 2
Q.1 If the roots of 2x2 + (4m +1) x + 2(2m – 1) = 0 are reciprocals of one another; find ‘m’.
a.- 1/2
b.- 1/4
c.1/4
d.1
Q.2 Find maximum/minimum values of function given, also find the value of x where maxima and Minima occurs: x2 – 6x +12.
a.Minimum at x = 0, value: -12
b.Maximum at x = 0, value: -12
c.Maximum at x = 3, value: 3
d.Minimum at x = 3, value: 3
Q.3 Find maximum/minimum values of function given, also find the value of x where maxima and Minima occurs: -3x2 – 18x + 1.
a.Maximum at x = -3, value: 28
b.Minimum at x = 3, value: 64
c.Maximum at x = 3, value: 32
d.Minimum at x = 6, value: 32
Q.4 If α and β are two roots of the quadratic equation ax2 – bx + c = 0 where a, b, c are constant and a ≠ 0, then the value of 1/α + 1/β is
a.c/b
b.c/a
c.-b/c
d.b/c
Q.5 If a and b are the roots of the equation t2 + t – 1 = 0, then what is the value of a3 + b3?
a.-1
b.-2
c.-3
d.-4
Q.6 If α & β are the roots of the equation x2 + Kx + K/8 = 0 such that α - β = √5. Then the value of K would be.
a.2, 5
b.-2, 5/2
c.-2, -5/2
d.2, -5/2
Q.7 The value of x2 − 8x + 17 can never be less than
a.0
b.1
c.10
d.17
Q.8 f(x) = ax2 + bx + c is a quadratic polynomial and the roots of f(x) = 0 are natural numbers such that one root is double of the other root. If ‘c’ is a perfect square, then
a.Both a and b are even
b.a is even and b is odd
c.a is odd and b is even
d.both a and b are odd
Q.9 One root of x2 + kx - 8 = 0 is square of the other, then find the value of k.
a.2
b.-2
c.8
d.-8
Q.10 The positive value of m for which the roots (α, β) of equation x2 + 4(m – 2)x + 27 = 0 are such that 3α = β is?
a.7
b.5
c.3
d.1
Q.11 If the roots of the equation 2x2 – 3ax + a = 0 are in the ratio 1 : 3, find ‘a’.
a.
b.
c.
d.0, 27
Q.12 For what value of m, will the equation x2 – (3m + 1)x + 3m = 0 have equal roots.
a.
b.
c.
d.m = -3
Q.13 If one root of the equation 2x2 – 9x + k = 0 is twice the other, then find the value of k.
a.7
b.9
c.13
d.11
Q. 14 Find the value of :-
a.
b.
c.
d.Cannot be determined
Q.15 The positive value of m for which the roots (α, β) of equation x2 + 4(m – 2)x + 27 = 0 are such that 3α = β is?
Q.16 If one root of the equation 4x2 – 13x + k = 0 is twelve times the other, find k.
a.1
b.2
c.3
d.4
e.5
Q.17 Find ‘a’ so that the sum of the roots of equation ax2 + 4x + 6a = 0 may be equal to their product.
a.
b.
c.
d.
Q.18 If the quadratic eq. x2 + 9x + k = 0 has only one real root, then k =?
a.
b.
c.
d.
Q.19 If and are the roots of the equation 2x2 + 5x + 6 = 0, find the value of
a.
b.
c.
d.
Q.20 If the sum of the roots of a quadratic equation is 3 and the sum of the squares of the roots is 29, then find the equation.
a.x2 – 3x + 10 = 0
b.x2 – 3x – 10 = 0
c.x2 + 7x – 14 = 0
d.x2 – 5x + 11 = 0
Q.21 If one root of the equation ax2 + bx + c = 0 is double of the other, then 2b2 = ?
a.2b2 = 9bc
b.2c2 = 9ab
c.2a2 = 9bc
d.2b2 = 9ac
Q.22 The equation x2 – 8x + b = 0 has equal roots, then the value of ‘b’ is?
a.b = 18
b.b = 16
c.b = 14
d.b = 20
Q.23 Solve 3x + 2 + 3 – x = 10
a.– 2, – 1
b.2, 0
c.2, – 1
d.– 2, 0
Q.24 Let 𝛼 and 𝛽 be the roots of the quadratic equation 4x2 + 16x + 15 = 0. Find the value of 𝛼3 + 𝛽3.
a.109
b.19
c.38
d.–19
Q.25 Evaluate :
a.
b.
c.
d.5
ANSWERS
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
D | D | A | D | D | B | B | A | B | B |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
B | A | B | B | 5 | C | B | A | B | B |
21 | 22 | 23 | 24 | 25 | |||||
D | B | D | D | B |
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