Question

Find the product of zero of cubic polynomial $p\left(x\right)=x^3+4x^2+x-6$.

Answer 1

We know that,

If $\alpha ,\beta$ and $\gamma$ are the zeros of a cubic polynomial $P\left(x\right)=a{x}^3+b{x}^2+cx+d,a\ne 0$ then,

Product of the zeros of $P\left(x\right)=\alpha \beta \gamma =\frac{-d}{a}$

Now, the given polynomial is $P\left(x\right)=x^3+4x^2+x-6$

Here, $a=1,b=4,c=1,$ and $d=-6$

$\Rightarrow$ product of zero of cubic polynomial $P\left(x\right)$

$\Rightarrow \alpha \beta \gamma =\frac{-d}{a}$

$\Rightarrow \alpha \beta \gamma =\frac{-(-6)}{1}=6$

Hence, the product of zero of cubic polynomial $6$.