EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2019 (21-Apr Shift-2)>Q 5

HARD

AP EAPCET

IMPORTANT

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If $α, β$ are the real roots of $x^{2} + p x + q = 0$ and $α^{4}, β^{4}$ are the roots of $x^{2} - r x + s = 0,$ then the equation $x^{2} - 4 q x + 2 q^{2} - r = 0$ has always

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Important Questions on Theory of Equations

MEDIUM

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2021 (19-Aug Afternoon)>Q 6

If

α, β

are the roots of

11 x^{2} + 12 x - 13 = 0

, then

\frac{1}{α^{2}} + \frac{1}{β^{2}} =

? (approximately close to)

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2021 (19-Aug Afternoon)>Q 7

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

A P,

then

A

and

B

are

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET - 20 Aug 2021 Forenoon>Q 8

If one root of the equation

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

is

(2 - i)

, then the other root is

MEDIUM

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET - 20 Aug 2021 Forenoon>Q 9

If

2, 1, 1

are roots of the equation

x^{3} - 4 x^{2} + 5 x - 2 = 0

, then the roots of

{(x + \frac{1}{3})}^{3}

- 4 {(x + \frac{1}{3})}^{2} + 5 (x + \frac{1}{3}) - 2 = 0

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET - 20 Aug 2021 Afternoon>Q 10

2 + \sqrt{5}, 1

are roots of the cubic equation given by

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2019 (21-Apr Shift-2)>Q 11

Let

θ

be an acute angle such that the equation

x^{3} + 4 x^{2} \cos θ + x \cot θ = 0

has multiple roots. Then the value of

θ

(in radians) is

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2018 (25-APR Shift-1)>Q 12

Let

a, b

and

c

be three positive real numbers such that the sum of any two of them is greater than the third. All the values of

λ

such that the roots of the equation

x^{2} + 2 (a + b + c) x + 3 λ (a b + b c + c a) = 0

are real, are given by

EASY

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2021 (19-Aug Afternoon)>Q 13

If

a

is a positive integer such that the roots of the equation

7 x^{2} - 13 x + a = 0

are rational numbers, then the smallest possible value of

a

is