Question

If the product of two zeros of the polynomial f(x) = 2$x^3$ + 6$x^2$ - 4x + 9 is 3 , then its third zero is

Answer 1

$f\left(x\right)=2x^3+6x^2-4x+9$

Let three zeroes be $\alpha ,\beta ,\gamma$

Product of $3$ zeroes$=\frac{-d}{a}=\frac{-9}{2}$

Given Product of $2$ zeroes $=3$

or $\alpha .\beta =3$

$\Rightarrow \alpha \beta \gamma =\frac{-9}{2}\Rightarrow 3\gamma =\frac{-9}{2}\Rightarrow \gamma =\frac{-3}{2}$

Third zero is $\frac{-3}{2}$