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If $α$ and $β$ are the zeros of the quadratic polynomial $f (x) = a x 2 + b x + c$ then evaluate $α 2 β + α β 2$ .

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− b c a 2

− b c b 2

b c a 2

− b c c 2

answer is A.

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Detailed Solution

Given that

α

and

β

are the zeroes of the quadratic polynomial

f (x) = a x 2 + b x + c .

Then sum and product of roots can be written as,

Sum of zeroes = − b a ⇒ α + β = − b a

And,Product = c a ⇒ α β = c a

Given to evaluate α 2 β + α β 2

⇒ α 2 β + α β 2 = α β (α + β)

Substitute

α + β = − b a and α β = c a

into the equation,

α 2 β + α β 2 = α β (α + β) = c a − b a = − b c a 2

Therefore value of

α 2 β + α β 2 is − b c a 2 .

Hence the correct option is 1.

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