Explanation
Step 1
factorize
[tex]\begin{gathered} f(x)=2x^3-6x^2-16x-20 \\ f(x)=2(x^3-3x^2-8x-10) \\ \end{gathered}[/tex]a)we know that
[tex]\begin{gathered} f(5)=0 \\ \text{hence,}5\text{ is a zero} \end{gathered}[/tex][tex]\begin{gathered} f(x)=2(x^3-3x^2-8x-10) \\ f(x)=2(x-5)(x^2+2x+2) \end{gathered}[/tex]Step 2
factorize the trinomial, use the quadratic formula
[tex]\begin{gathered} x^2+2x+2=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-2\pm\sqrt[]{2^2-4\cdot2\cdot1}}{2\cdot1} \\ x=\frac{-2\pm\sqrt[]{-4}}{2} \\ x=\frac{-2\pm\sqrt[]{-4}}{2} \\ x_1=\frac{-2+2i}{2}=-1+i \\ x_2=\frac{-2-2i}{2}=-1-i \end{gathered}[/tex]therefore, the zeros are:
[tex]\begin{gathered} x=5 \\ x=-1+i \\ x=-1-i \end{gathered}[/tex]I hope this helps you
