Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 147

HARD

JEE Advanced

IMPORTANT

Earn 100

If $α$ and $β$ are the roots of quadratic equation $x^{2} - 2 \cos θ x + 1 = 0,$ then the equation whose roots are $α^{n}, β^{n}$ is

50% studentsanswered this correctly

Important Questions on Inequalities and Quadratic Equation

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 148

If

1, ω, ω^{2}, \dots, ω^{n - 1}

are the

n^{t h}

roots of unity, then

(1 + ω) (1 + ω^{2}) \dots (1 + ω^{n - 1})

equals

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 149

If

f (x) = x^{4} + 9 x^{3} + 35 x^{2} - x + 4,

then

f (- 5 + 2 \sqrt{- 4})

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 150

If

p \in [- 1, 1],

then the value of

x

for which

4 x^{3} - 3 x - p = 0

has a root lies in

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 151

If

α, β, γ

and

σ

are the roots of the equation

x^{4} + 4 x^{3} - 6 x^{2} + 7 x - 9 = 0,

then the value of

(1 + α^{2}) (1 + β^{2}) (1 + γ^{2}) (1 + σ^{2})

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 152

If

\tan θ_{1}, \tan θ_{2}

and

\tan θ_{3}

are the real roots of the

x^{3} - (a + 1) x^{2} + (b - a) x - b = 0,

where

θ_{1} + θ_{2} + θ_{3} \in (0, π)

. Then,

θ_{1} + θ_{2} + θ_{3}

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 153

If

α, β

and

γ

are the roots of

x^{3} - x^{2} - 1 = 0,

then

\frac{1 + α}{1 - α} + \frac{1 + β}{1 - β} + \frac{1 + γ}{1 - γ}

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 154

The equation formed by decreasing each root of

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

by

1

is

2 x^{2} + 8 x + 2 = 0,

then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 155

If the equations

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

and

x^{2} + x + 1 = 0

have a common roots, then