EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Theory of Equation>WBJEE 2018>Q 1

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If the equation $x^{2} - c x + d = 0$ has roots equal to the fourth powers of the roots of $x^{2} + a x + b = 0,$ where $a^{2} > 4 b,$ then the roots of $x^{2} - 4 b x + 2 b^{2} - c = 0$ will be

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Important Questions on Theory of Equation

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Theory of Equation>WBJEE 2020>Q 2

The expression

a x^{2} + b x + c, (a, b

and

c

are real

)

has the same sign as that of

a

for all

x

if

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Theory of Equation>WBJEE 2020>Q 3

Let

A = (\begin{array}{l} a & b \\ c & d \end{array})

be a

2 \times 2

real matrix with

det A = 1 .

If the equation

det (A - λ I_{2}) = 0

has imaginary roots (

I_{2}

be the identity matrix of order

2

), then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Theory of Equation>WBJEE 2020>Q 4

Let

z_{1}

and

z_{2}

be two imaginary roots of

z^{2} + p z + q = 0,

where

p

and

q

are real. The points

z_{1}, z_{2}

and origin form an equilateral triangle if

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Theory of Equation>WBJEE 2020>Q 5

If

P (x) = a x^{2} + b x + c

and

Q (x) = - a x^{2} + d x + c

, where

a c \neq 0

(

a, b, c, d

are all real), then

P (x) \cdot Q (x) = 0

has

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Theory of Equation>WBJEE 2018>Q 6

If

b_{1} b_{2} = 2 (c_{1} + c_{2})

and

b_{1}, b_{2}, c_{1}, c_{2}

are all real numbers, then at least one of the equations

x^{2} + b_{1} x + c_{1} = 0

and

x^{2} + b_{2} x + c_{2} = 0

has

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Theory of Equation>WBJEE 2019>Q 7

Let

a, b, c

be real numbers such that

a + b + c < 0

and the quadratic equation

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

has imaginary roots. Then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Theory of Equation>WBJEE 2019>Q 8

Let

f

and

g

be differentiable on the interval

I

and let

a, b \in I, a < b .

Then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Theory of Equation>WBJEE 2020>Q 9

Let

f (x) = x^{13} + x^{11} + x^{9} + x^{7} + x^{5} + x^{3} + x + 12

. Then