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

HARD

CAT

IMPORTANT

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If roots of equation $x^{2} - 2 a x + (a^{2} + a - 3) = 0$ are real and less than $3,$ then

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Important Questions on Theory of Equations

EASY

CAT

IMPORTANT

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

Let

α, β (α < β)

are roots of the equation

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

where

c < 0 < b,

then

HARD

CAT

IMPORTANT

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

If

b > a,

then the equation

(x - a) (x - b) - 1 = 0,

has

HARD

CAT

IMPORTANT

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

Let

α, β

be the roots of

x^{2} - x + p = 0

and

γ, δ

be the roots of

x^{2} - 4 x + q = 0 .

If

α, β, γ, δ

are in

G P

, then the integer values of

p

and

q

respectively are

HARD

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 18

If

α, β

are the roots of the equation

x^{2} - p x + q = 0

, then find the quadratic equation the roots of which are

(α^{2} - β^{2}) (α^{3} - β^{3})

&

α^{3} β^{2} + α^{2} β^{3}

.

HARD

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 19

Given that

α, γ

are roots of the equation

A x^{2} - 4 x + 1 = 0

, and

β, δ

the roots of the equation

B x^{2} - 6 x + 1 = 0

, then values of

A

and

B

such that

α, β, γ

and

δ

are in

H . P .

, are

EASY

CAT

IMPORTANT

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

Let

a, b, c

be real numbers such that

a + b + c = 0

, then

EASY

CAT

IMPORTANT

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

Given that

p

and

q

are prime, the equation

{px}^{2} - qx + q = 0

has

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 23

The equation

x^{4} - {px}^{3} + q = 0

has an integral root. Find this only integral root if

p

and

q

are prime numbers.