EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>TS EAMCET 2020 (9-Sep Shift-1)>Q 10

MEDIUM

TS EAMCET

IMPORTANT

Earn 100

Assertion $(A) : 3 x^{2} - 16 x + 4 > - 16$ is satisfied for some values of real $x$ in $(0, \frac{10}{3})$ .

Reason $(R) : a x^{2} + b x + c$ and $a$ will have the same sign for some values of $x \in R$ when $b^{2} - 4 a c > 0$ .

The correct option among the following is

38.24% studentsanswered this correctly

Important Questions on Theory of Equations

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>TS EAMCET - 5 August 2021 Shift 2>Q 11

f (x) = a x^{2} - b x - a

is a quadratic expression. If

K

is the least real number such that

f (x) \leq K, \forall x \in R,

then

EASY

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>TS EAMCET 2021 (04-Aug Shift-2)>Q 12

The smallest negative integer satisfying both the quadratic inequalities

x^{2} < 4 x + 77

and

x^{2} > 4

is

EASY

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>TS EAMCET - 5 August 2021 Shift 1>Q 13

If

x^{2} - 5 x - 14 > 0 \Rightarrow x

lie outside

[α, β],

then

\frac{α}{β} =

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>TS EAMCET 2021 (04-Aug Shift-1)>Q 14

If

y = \frac{x^{2} + 14 x + 9}{x^{2} + 2 x + 3} \forall x \in ℝ,

then the interval of maximum length in which

y

lies is

HARD

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>TS EAMCET 2018 (04-May Shift-1)>Q 15

If the roots of the equation

x^{2} + x + a = 0

exceed

a

, then

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>TS EAMCET 2020 (9-Sep Shift-1)>Q 16

Let

α, β, γ

be the roots of the equation

x^{3} + p x + q = 0

and

f (x) = 3 p^{2} x^{2} + p^{2} x + 3 q

. Then

\sum α^{2} β + \sum α^{4} =

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>TS EAMCET 2020 (9-Sep Shift-1)>Q 17

If

α, β, γ

are the roots of the equation

x^{3} + a x^{2} - b x + c = 0

, then

\sum β^{2} (γ + α) =

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Theory of Equations>TS EAMCET 2018 (04-May Shift-1)>Q 18

If the roots of the equation

\sqrt{\frac{x}{1 - x}} + \sqrt{\frac{1 - x}{x}} = \frac{5}{2}

are

p

and

q (p > q)

and the roots of the equation

(p + q) x^{4} - p q x^{2} + \frac{p}{q} = 0

are

α, β, γ, δ

, then

{(Σ α)}^{2} - Σ α β + α β γ δ =