Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 2

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IMPORTANT

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If $x = 1 + i$ is a root of the equation $x^{3} - i x + 1 - i = 0,$ then the other real root is (where $i = \sqrt{- 1}$ )

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Important Questions on Quadratic Equations

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 3

The number of roots of the equation

\sqrt{x - 2} (x^{2} - 4 x + 3) = 0

is

MEDIUM

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IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 4

Let

p

and

q

be roots of the equation

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

and let

r

and

s

be the roots of the equation

x^{2} - 18 x + B = 0 .

If

p < q < r < s

are in arithmetic progression, then the values of

A

and

B

are

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 5

If

α, β

be the roots of the equation

2 x^{2} - 35 x + 2 = 0,

then the value of

{(2 α - 35)}^{3} {(2 β - 35)}^{3}

is equal to

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 6

The sum of values of

x

satisfying the equation

{(31 + 8 \sqrt{15})}^{x^{2} - 3} + 1 = {(32 + 8 \sqrt{15})}^{x^{2} - 3}

is

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IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 7

A quadratic equation whose product of roots

x_{1}

and

x_{2}

is equal to

4

and satisfying the relation

\frac{x_{1}}{(x_{1} - 1)} + \frac{x_{2}}{(x_{2} - 1)} = 2

is

EASY

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 8

The integral values of

m

for which the roots of the equation

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

are rational are given by the expression [where

n

is integer]

HARD

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 9

Suppose

A, B, C

are defined as

A = a^{2} b + a b^{2} - a^{2} c - a c^{2}, B = b^{2} c + b c^{2} - a^{2} b - a b^{2}

and

C = a^{2} c + a c^{2} - b^{2} c - b c^{2},

where

a > b > c > 0

and the equation

A x^{2} + B x + C = 0

has equal roots, then

a, b and c

are in

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 10

If

α

and

β, α

and

γ, α

and

δ

are the roots of the equations

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

and

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

respectively, where

a, b

and

c

are positive real numbers, then

α + α^{2} =