Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>EXERCISE 5.1>Q 9

EASY

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IMPORTANT

Earn 100

If $α$ and $β$ are the roots of the equation $x^{2} - 7 x + 1 = 0$ then find the value of $\frac{1}{(α - 7)^{2}} + \frac{1}{(β - 7)^{2}}$ .

Important Questions on Quadratic Equations

EASY

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>EXERCISE 5.1>Q 10

Find the sum of all real roots of the equation

(x - 2)^{2} + | x - 2 | - 2 = 0

.

MEDIUM

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>EXERCISE 5.2>Q 11

The real value of

a

for which the sum of the squares of the roots of the equation

x^{2} - (a - 2) x - a - 1 = 0

assumes the least value, is

EASY

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>EXERCISE 5.2>Q 12

Let

F (x) = x^{2} + 4 x + 1

. Then

MEDIUM

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>EXERCISE 5.2>Q 13

If

x \in R

then

\frac{x^{2} + 2 x + a}{x^{2} + 4 x + 3 a}

can take all real values if;

EASY

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>EXERCISE 5.2>Q 14

If the real roots

α

and

β

of the equation

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

are real and of opposite sign then the roots of the equation

α (x - β)^{2} + β (x - α)^{2}

is/are

EASY

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>EXERCISE 5.2>Q 15

If

1

lies between the roots of the equation

3 x^{2} - 3 \sin α x - 2 \cos^{2} α = 0

then

α

lies in the interval

EASY

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>EXERCISE 5.2>Q 16

The value of

λ

for which the equation

2 x^{2} - 2 (2 λ + 1) x + λ (λ + 1) = 0

may have one root less than

λ

and other root greater than

λ

are given by

EASY

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>EXERCISE 5.2>Q 17

If

(4 a + c)^{2} < 4 b^{2}

then one root of

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

lies in