Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-1>Q 20

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The value of $a$ ' for which the sum of the squares of the roots of $2 x^{2} - 2 (a - 2) x - a - 1 = 0$ is least, is

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Important Questions on Quadratic Equations

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-1>Q 21

If the roots of the quadratic equation

x^{2} + 6 x + b = 0

are real and distinct and they differ by at most

4

, then the least value of

b

is

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-1>Q 22

The expression

\frac{x^{2} + 2 x + 1}{x^{2} + 2 x + 7}

lies in the interval;

(x \in R) -

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-1>Q 23

If the roots of the equation

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

are real and less than

3

, then

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-1>Q 24

The number of integral values of

m

, for which the roots of

x^{2} - 2 m x + m^{2} - 1 = 0

will lie between

- 2

and

4

is

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-1>Q 25

If the roots of the equation,

x^{3} + P x^{2} + Q x - 19 = 0

are each one more than the roots of the equation,

x^{3} - A x^{2} + B x - C = 0

, where

A, B, C, P & Q

are constants then the value of

A + B + C =

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-1>Q 26

If

α, β, γ, δ

are roots of

x^{4} - 100 x^{3} + 2 x^{2} + 4 x + 10 = 0

, then

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

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-1>Q 27

Number of real solutions of the equation

x^{4} + 8 x^{2} + 16 = 4 x^{2} - 12 x + 9

is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-1>Q 28

Solution set of the inequality,

2 - \log_{2} (x^{2} + 3 x) \geq 0

is