Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 21

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KVPY Aptitude Test - Stream SA

IMPORTANT

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The number of values of $k$ for which $[x^{2} - (k - 2) x + k^{2}] \cdot [x^{2} + k x + (2 k - 1)]$ is a perfect square is

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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 22

If

α, β

are the roots of

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

and

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

and if

(\frac{α}{β}), (\frac{β}{α})

are the roots of

x^{n} + 1 + {(x + 1)}^{n} = 0,

then

n (\in N)

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 23

If

x y = 2 (x + y), x \leq y

and

x, y \in N

, then the number of solutions of the equation are

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KVPY Aptitude Test - Stream SA

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 24

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

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KVPY Aptitude Test - Stream SA

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 25

The number of real solutions of the equation

{(\frac{9}{10})}^{x} = - 3 + x - x^{2}

is

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 26

If the equation

\cot^{4} x - 2 {cosec}^{2} x + a^{2} = 0

has at least one solution then, sum of all possible integral values of

a

is equal to

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 27

If the quadratic equation

4 x^{2} - 2 (a + c - 1) x + a c - b = 0; (a > b > c)

is given, then

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KVPY Aptitude Test - Stream SA

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 28

If the equation

|x^{2} + b x + c| = k

has four real roots, then

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KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 29

P (x)

is a polynomial with integral coefficients such that for four distinct integers

a, b, c, d : P (a) = P (b) = P (c) = P (d) = 3

. If

P (e) = 5

(

e

is an integer), then