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Zeroes of a Quadratic Polynomial

If α and ...

Question

If $α$ and $β$ are the zeroes of the quadratic polynomial $p (x) = a x^{2} + b x + c, (a \neq 0)$ then $α . β =$

A

\frac{b}{a}

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B

\frac{c}{a}

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C

\frac{- b}{a}

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D

\frac{- c}{a}

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Solution

The correct option is B $\frac{c}{a}$
For zeros of polynomial $a x^{2} + b x + c$
We must have $a x^{2} + b x + c = 0$
If $α, β$ are zeros of $p (x)$
then $α, β$ must be roots of above quadratic
Hence product of roots(zeros here) $= \frac{c}{a}$

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