Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 157

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JEE Advanced

IMPORTANT

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If the equations $a x^{2} + b x + c = 0$ and $c x^{2} + b x + a = 0, a \neq c$ have a negative common root, then the value of $a - b + c$ 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>Target Exercises>Q 158

If the equations

x^{2} + i x + a = 0

and

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

a \neq 0

have a common root, then

a

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 159

If the equations

x^{2} + 2 x + 3 λ = 0

and

2 x^{2} + 3 x + 5 λ = 0

have a non-zero common root, then

λ

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 160

If the equations

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

and

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

have a common root, then

a : b : c

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 161

If the equations

x^{2} - p x + q = 0

and

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

have a common root and the other root of the second equation is the reciprocal of the other root of the first, then

{(q - b)}^{2}

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 162

Let

f (x) = 1 + 2 x + 3 x^{2} + \dots + (n + 1) x^{n},

where

n

is even. Then, the number of real roots of the equation

f (x) = 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>Target Exercises>Q 163

The value of

x^{2} + 2 b x + c

is positive, if

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 164

If

a x^{2} + b x + 10 = 0

does not have two distinct real roots, then the least value of

5 a + b

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 165

If

- a^{2} x^{2} + 2 x + 3 a^{2} > 0, \forall x \in (2, 4),

then the values of

a

lie in the interval