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

HARD

AP EAPCET

IMPORTANT

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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

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Important Questions on Theory of Equations

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

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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

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 14

For

a \neq b

, if the equation

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

and

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

have a common root, then the value of

a + b =

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 15

\{x \in ℝ : \frac{\sqrt{6 + x - x^{2}}}{2 x + 5} \geq \frac{\sqrt{6 + x - x^{2}}}{x + 4}\} =

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2021 (19-Aug Forenoon)>Q 16

n \in N

then the statement

8 n + 16 \leq 2^{n}

is true for

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2018 (25-APR Shift-1)>Q 17

Let

f (x) = (x - a) (x - b) - (\frac{a + b}{2}) .

If

f (x) = 0

has both non-negative roots, then the minimum value of

f (x)

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2020 (Sep-23 Shift-1)>Q 18

If

α, β, γ

are the roots of

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

, then find

\sum α β (α + β)

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>AP EAPCET 2020 (Sep-23 Shift-1)>Q 19

If the bi-quadratic equation

f (x) = x^{4} + 2 x^{3} - 16 x^{2} - 22 x + 7 = 0

has

2 + \sqrt{3}

as one of its roots, then which of the following is not a root of

f (x) ?