Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 8

MEDIUM

CAT

IMPORTANT

Earn 100

The number of quadratic equations that are unchanged by squaring their roots is

47.59% studentsanswered this correctly

Important Questions on Theory of Equations

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 11

If

x \in R,

and

K = \frac{(x^{2} - x + 1)}{(x^{2} + x + 1)},

then:

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 15

If

α, β, γ

are such that

α + β + γ = 2, α^{2} + β^{2} + γ^{2} = 6, α^{3} + β^{3} + γ^{3} = 8,

then

α^{4} + β^{4} + γ^{4}

is

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 16

The real values of a for which the quadratic equation 2x² - (a³ + 8a - 1) x + a² - 4a = 0 possesses roots of opposite signs are given by :

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 17

If

α, β

are the roots of

a x^{2} + b x + c = 0

and

α + h, β + h

are the roots of

p x^{2} + q x + r = 0,

then what is

h

equal to?

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 20

The value of

a

for which the equation

x^{2} - 2 (a - 1) x + (2 a + 1) = 0

has both roots positive is

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 21

The number of real solutions of the equation

2^{3 x^{2} - 7 x + 4} = 1

is:

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 22

The number of real solutions of the equation

2 | x |^{2} - 5 | x | + 2 = 0

is:

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 24

The given equation

\sqrt{x + 1} - \sqrt{x - 1} = \sqrt{4 x - 1}

has