Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Work Book Exercise 5.5>Q 6

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JEE Advanced

IMPORTANT

Earn 100

If $a x^{2} + b x + 6 = 0$ does not have two distinct real roots, then the least value of $3 a + b$ 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>Work Book Exercise 5.5>Q 7

If

x

is real, then the least value of the expression

\frac{x^{2} - 6 x + 5}{x^{2} + 2 x + 1}

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Work Book Exercise 5.5>Q 8

If the quadratic equation

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

has imaginary roots, then

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Work Book Exercise 5.5>Q 9

Let

S

denote the set of real values of

a

, for which the roots of the equation

x^{2} - a x - a^{2} = 0

exceeds

a

. Then,

S

equals

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Work Book Exercise 5.5>Q 10

x^{4} - 4 x - 1 = 0

has

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Work Book Exercise 5.5>Q 11

The roots

α

and

β

of the quadratic equation are

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

are real and of opposite sign. Then, the roots of the equation

α {(x - β)}^{2} + β {(x - α)}^{2} = 0

are

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Work Book Exercise 5.5>Q 13

If

0 < a < 5, 0 < b < 5

and

\frac{x^{2} + 5}{2} = x - 2 \cos (a + b x)

is satisfied for at least one real

x

, then the greatest value of

a + b

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Work Book Exercise 5.5>Q 14

If the roots of

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

change by the same quantity, then the expression in

a, b

and

c

that does not change is

MEDIUM

JEE Advanced

IMPORTANT

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

The least integer satisfying

49.4 - (\frac{27 - x}{10}) < 47.4 - (\frac{27 - 9 x}{10})

is