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

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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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Important Questions on Quadratic Equations

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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

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 1

Let

α, β, γ

be the roots of the equation

x^{3} + 3 a x^{2} + 3 b x + c = 0

. If

α, β, γ

are in H.P. then

β

is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 3

Number of solution(s) satisfying the equation

3 x^{2} - 2 x^{3} = \log_{2} (x^{2} + 1) - \log_{2} x

is

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

Number of roots of the equation

x^{2} \cdot e^{2 - |x|} = 1

is

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 5

The equation whose roots are

\sec^{2} α & {cosec}^{2} α

can be -

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 6

If $\cos α$ is a root of the equation $25 x^{2} + 5 x - 12 = 0, - 1 < x < 0$ , then the value of $\sin 2 α$ is

$(A)$ $\frac{12}{25}$

$(B) \frac{- 12}{25}$

$(C) \frac{- 24}{25}$

$(D) \frac{24}{25}$

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 7

If the roots of the equation

\frac{1}{x + p} + \frac{1}{x + a} = \frac{1}{r}

are equal in magnitude and opposite in sign, then

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 8

Graph of $y = a x^{2} + b x + c$ is given adjacently. What conclusions can be drawn from this graph -

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