Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 12

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Let $p (x)$ be the cubic polynomial $7 x^{3} - 4 x^{2} + K$ . Suppose the three roots of $p (x)$ form an arithmetic progression. Then the value of $k$ , 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 13

If the quadratic equation

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

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

2 a + b

is

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 15

The value of '

a

' for which the expression

y = x^{2} + 2 a \sqrt{a^{2} - 3} x + 4

is perfect square, is

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 17

The correct statement is / are -

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 18

If

α_{1} < α_{2} < α_{3} < α_{4} < α_{5} < α_{6}

, then the equation

(x - α_{1}) (x - α_{3}) (x - α_{5}) + 3 (x - α_{2}) (x - α_{4}) (x - α_{6}) = 0

has

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 20

The value(s) of '

b

' for which the equation,

2 \log_{\frac{1}{25}} (b x + 28) = - \log_{5} (12 - 4 x - x^{2})

has coincident roots, is/are

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 21

For every

x \in R

, the polynomial

x^{8} - x^{5} + x^{2} - x + 1

is -

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

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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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 -