Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 41

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If $a > b > 0$ and $a^{3} + b^{3} + 27 a b = 729$ , then the quadratic equation $a x^{2} + b x - 9 = 0$ has roots $α & β$ , $(α < β)$ . Find the value of $4 β - a α$ .

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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 45

If the roots of the equation

x^{3} + P x^{2} + Q x - 19 = 0

are each one more than the roots of the equation

x^{3} - A x^{2} + B x - C = 0,

where

A, B, C, P & Q

are constants, then the value of

A + B + C

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 46

If one root of the equation

t^{2} - (12 x) t - (f (x) + 64 x) = 0

is twice of other, then find the maximum value of the function

f (x)

, where

x \in R

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 48

Find the least value of

7 a

for which at least one of the roots of the equation

x^{2} - (a - 3) x + a = 0

is greater than

2

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 52

Possible values of

p

for which the equation

(p^{2} - 3 p + 2) x^{2} - (p^{2} - 5 p + 4) x + p - p^{2} = 0

does not possess more than two roots is/are

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 53

If

a, b

are non-zero real numbers and

α, β

are the roots of

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

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 54

If

α, β

are the roots of

a x^{2} + b x + c = 0 (a \neq 0)

and

α + δ, β + δ

are the roots of

A x^{2} + B x + C = 0 (A \neq 0)

for some constant

δ,

then

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

If one root of the equation

4 x^{2} + 2 x - 1 = 0

is

{}^{'}α^{'},

then

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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