Question

The polynomial 73 – 672 – 27% + 140 can be factored as(z. – 4) (z - 7) (z + 5). What are the roots of the polynomial?Enter the roots as integers or decimals. If there is more than onesolution, separate them by commas.

Answer 1

Given:

The give polynomial is factored as :

$(z-4)(z-7)(z+5)_{}$

Now, the roots of the polynomial are given as:

put each factor equal to zero and find value of z, that is,

$\begin{gathered} (z-4)=0\Rightarrow z=4 \\ (z-7)=0\Rightarrow z=7 \\ (z+5)=0\Rightarrow z=-5 \end{gathered}$

Hence, the roots are z= -5,4,7.

This is the required answer.