Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 50

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

The equation whose roots are the squares of the roots of the equation $2 x^{2} + 3 x + 1 = 0$ , is

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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>Entrances Gallery>Q 51

In a

Δ A B C, \tan A

and

\tan B

are the roots of

p q (x^{2} + 1) = r^{2} x .

Then,

Δ A B C

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 53

The number of solution(s) of the equation

\sqrt{x + 1} - \sqrt{x - 1} = \sqrt{4 x - 1}

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 54

If

9 \sqrt{x} = \sqrt{12} + \sqrt{147},

then the value of

x

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 55

Solve the equation

x^{2} - \sqrt{3} x + 1 = 0

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 56

_{If $a = \cos \frac{2 π}{7} + i \sin \frac{2 π}{7},$ then the quadratic equation whose roots are $α = a + a^{2} + a^{4}$ and $β = a^{3} + a^{5} + a^{6},$}

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 57

Let

p

and

q

be real numbers. If

α

is the root of

x^{2} + 3 p^{2} x + 5 q^{2} = 0, β

is the root of

x^{2} + 9 p^{2} x + 15 q^{2} = 0

and

0 < α < β,

then the equation

x^{2} + 6 p^{2} x + 10 q^{2} = 0

has a root

γ

that always satisfies

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 58

If the roots of the equation

λ^{2} + 8 λ + μ^{2} + 6 μ = 0

are real, then

μ

lies between

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 59

The number of solutions of the inequality

|x - 2| + |x + 2| < 4

is