Given the polynomial:
[tex]f(x)=2x^3+10x^2+18x+10[/tex]We know that (x + 1) is a factor of f(x). We divide f(x) by (x + 1):
Then:
[tex]f(x)=(x+1)(2x^2+8x+10)=2(x+1)(x^2+4x+5)[/tex]For the quadratic term, we solve the following equation:
[tex]x^2+4x+5=0[/tex]Using the general solution for quadratic equations:
[tex]\begin{gathered} x=\frac{-4\pm\sqrt{4^2-4\cdot1\cdot5}}{2\cdot1}=\frac{-4\pm\sqrt{16-20}}{2}=\frac{-4\pm\sqrt{4}}{2} \\ \\ \therefore x=-2\pm i \end{gathered}[/tex]The zeros of f(x) are:
[tex]\begin{gathered} x_1=-1 \\ \\ x_2=-2-i \\ \\ x_3=-2+i \end{gathered}[/tex]
