Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 55

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If one root of the equation $4 x^{2} + 2 x - 1 = 0$ is ${}^{'}α^{'},$ then

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Important Questions on Quadratic Equations

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 56

If

α, β

are the roots of

x^{2} + 3 x + 1 = 0,

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 57

If both roots of

x^{2} - 32 x + c = 0

are prime numbers, then possible values of

c

are

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 58

Let

f (x) = x^{2} - a (x + 1) - b = 0, a, b \in R - {0}, a + b \neq 0

. If

α

and

β

are roots of equation

f (x) = 0,

then the value of

\frac{1}{α^{2} - a α} + \frac{1}{β^{2} - a β} - \frac{2}{a + b}

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 59

If

f (x)

is a polynomial of degree three with leading coefficient

1

such that

f (1) = 1, f (2) = 4, f (3) = 9,

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 60

Let

P (x) = x^{32} - x^{25} + x^{18} - x^{11} + x^{4} - x^{3} + 1

. Which of the following are CORRECT?

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 61

If

α, β

are the real and distinct roots of

x^{2} + p x + q = 0

and

α^{4}, β^{4}

are the roots of

x^{2} - r x + s = 0

, then the equation

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

always has

(α \neq - β)

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 62

If

- 5 + i β, - 5 + i γ

(where

β^{2} \neq γ^{2}; β, γ \in R

and

i^{2} = - 1

) are roots of

x^{3} + 15 x^{2} + c x + 860 = 0, c \in R,

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 63

Let

f (x) = a x^{2} + b x + c > 0, \forall x \in R

or

f (x) < 0, \forall x \in R

. Which of the following is/are CORRECT?