EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2018 (25-APR Shift-1)>Q 21

MEDIUM

AP EAPCET

IMPORTANT

Earn 100

If the sum of any two roots of the equation $x^{3} + p x^{2} + q x + r = 0$ is zero, then

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Important Questions on Theory of Equations

EASY

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2021 (19-Aug Forenoon)>Q 22

If

{(x^{2} + 5 x + 5)}^{x + 5} = 1

then the number of integers satisfying this equation is

EASY

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2021 (19-Aug Forenoon)>Q 23

Let

f (x) = x^{3} + a x^{2} + b x + c

be polynomial with integer coefficients. If the roots of

f (x)

are integer and are in Arithmetic Progression, then

' a'

cannot take the value

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2021 (19-Aug Forenoon)>Q 24

The sum of the roots of the equation

e^{4 t} - 10 e^{3 t} + 29 e^{2 t} - 22 e^{t} + 4 = 0

is

EASY

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2021 (19-Aug Afternoon)>Q 25

Value of

a

for which equations

x^{3} + a x + 1 = 0

and

x^{4} + a x^{2} + 1 = 0

have a common root

EASY

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET - 20 Aug 2021 Forenoon>Q 26

Given

\frac{3 x - 2}{(x + 1)^{2} (x + 3)} = \frac{A}{x + 1} + \frac{B}{(x + 1)^{2}} + \frac{C}{x + 3}

, then

4 A + 2 B + 4 C

MEDIUM

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET - 20 Aug 2021 Afternoon>Q 27

If the product of the roots of

9 x^{3} + 112 x^{2} - 120 x + a = 0

is

12

, then the value of

{}^{'}a^{'}

is