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

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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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Important Questions on Quadratic Equations

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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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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 10

If

x^{2} + p x + 1

is a factor of the expression

a x^{3} + b x + c

then -

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Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-2>Q 11

The set of values of '

a

' for which the inequality

(x - 3 a) (x - a - 3) < 0

is satisfied for all

x

in the interval

1 \leq x \leq 3

.

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

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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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