Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 75

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JEE Advanced

IMPORTANT

Earn 100

The number of integral values of $b$ , for which the equation $x^{2} + b x - 16 = 0$ has integral roots, is

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Important Questions on Inequalities and Quadratic Equation

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 76

If

a, b

and

c

are three real numbers such that

a + 2 b + 4 c = 0 .

Then, the equation

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

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 77

If one of the roots of

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

is

3

and another equation

2 x^{2} - c x + d = 0

has equal roots, where

c

and

d

are real numbers, then

d

is equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 78

The value of

\frac{\{{(\sqrt{\sqrt{3} + 1} + \sqrt{\sqrt{3} - 1})}^{2}\} (\sqrt{3} - \sqrt{2})}{{(\sqrt{\sqrt{3} + 1})}^{2} - {(\sqrt{\sqrt{3} - 1})}^{2}}

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 79

If

| 2 x - 3 | < | x + 5 |

, then

x

lies in the interval

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 80

If

α

and

β

are the roots of the equation

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

then the equation whose roots are

\frac{k}{α}

and

\frac{k}{β}

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 81

If

3 \leq 3 t - 18 \leq 18

, then which one of the following is correct ?

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 82

The solution set of the inequation

\frac{x + 11}{x - 3} > 0

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 83

In a right angled triangle, the sides are

a, b

and

c

, with

c

as hypotenuse and

c - b \neq 1, c + b \neq 1 .

Then, the value of

\frac{(\log_{c + b} a + \log_{c - b} a)}{(2 \log_{c + b} a \times \log_{c - b} a)}

will be