Question

If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $p\left(x\right)=a{x}^2+bx+c,(a\ne 0)$ then $\alpha .\beta =$

• A. $\frac{b}{a}$
• B. $\frac{c}{a}$
• C. $\frac{-b}{a}$
• D. $\frac{-c}{a}$

Answer 1

The correct option is B $\frac{c}{a}$

For zeros of polynomial $a{x}^2+bx+c$

We must have $a{x}^2+bx+c=0$

If $\alpha ,\beta$ are zeros of $p\left(x\right)$

then $\alpha ,\beta$ must be roots of above quadratic

Hence product of roots(zeros here)$=\frac{c}{a}$