Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 22

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If $α, β$ are the roots of the quadratic equation $(p^{2} + p + 1) x^{2} + (p - 1) x + p^{2} = 0$ such that unity lies between the roots then the set of values of $P$ 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-2>Q 23

Three roots of the equation,

x^{4} - p x^{3} + q x^{2} - r x + s = 0

are

\tan A, \tan B & \tan C

where

A, B, C

are the angles of a triangle. The fourth root of the biquadratic is -

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 24

If

α

is a root of the equation

2 x (2 x + 1) = 1

, then the other root is -

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 25

If

b^{2} \geq 4 a c

for the equation

a x^{4} + b x^{2} + c = 0

, then all roots of the equation will be real if

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 26

Let

α, β

be the roots of

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

, where

a & b \in R

. If

α + 3 β = 0

, then -

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-3>Q 18

If one non-zero root of the quadratic equation

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

be the square of the other, then the value of

\frac{b^{3} + a^{2} c + a c^{2}}{a b c}

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-3>Q 20

The product of the real roots of the equation,

x^{2} + 18 x + 30 = 2 \sqrt{x^{2} + 18 x + 45}

, is

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-3>Q 21

Maximum integral value

' a'

such that

f (x) = \frac{a x^{2} + 2 (a + 1) x + 9 a + 4}{x^{2} - 8 x + 32}

is always negative, is

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-3>Q 22

Number of integral values of

‘ a ’

for which

- 3 < \frac{x^{2} + a x - 2}{x^{2} + x + 1} < 2

is valid for all real

x

, is