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If $α$ and $β$ are the zeros of the quadratic polynomial $p x = 4 x 2 − 5 x − 1$ , find the value $α 2 β + α β 2 .$

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416

− 416

− 516

516

answer is C.

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Detailed Solution

Given

α

and

β

are the zeros of the quadratic polynomial

p x = 4 x 2 − 5 x − 1.

α

and

β

are zeroes of quadratic polynomial

p x = a x 2 + b x + c

, where

a = 4

b = − 5,

and

c = − 1

,then,

Sum = − b a

⇒ α + β = − b a = − (− 5) 4 = 54

∴ α + β = 54

Product = c a

⇒ α β = c a = − 14

∴ α β = − 14

Now,

α 2 β + α β 2 = α β (α + β)

Substitute

α + β = 54

and

α β = − 14

into the equation,

⇒ α 2 β + α β 2 = α β (α + β) = − 14 × 54 = − 516

Therefore value of

α 2 β + α β 2 is − 516 .

Hence the correct option is 3.

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