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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 $β a α + b + α a β + b$ .

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− 2 a

2 a

− 2 b

2 b

answer is A.

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Detailed Solution

Given that

α

and

β

are the zeroes of the given 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

β a α + b + α a β + b can be written as,

Substitute

α + β = − b a and α β = c a

into the equation, Question Image

β a α + b + α a β + b = − b 2 / a + b 2 − 2 a c / a a c = − b 2 + b 2 − 2 a c a 2 c = − 2 a c a 2 c = − 2 a

Therefore value of

β a α + b + α a β + b is − 2 a

.
Hence the correct option is 1.

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