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Given:
[tex]F\left(x\right)=x^3+x^2+9x+9[/tex]To find:
The zeros
Explanation:
Factorizing by grouping method,
[tex]\begin{gathered} F\left(x\right)=x^3+x^2+9x+9 \\ =x^2(x+1)+9(x+1) \\ =(x+1)(x^2+9) \end{gathered}[/tex]The zeros are found by equating the factors with zero.
[tex]\begin{gathered} x+1=0 \\ x=-1 \end{gathered}[/tex]And we have,
[tex]\begin{gathered} x^2+9=0 \\ x^2=-9 \\ x=\pm\sqrt{-9} \\ x=\pm3i \end{gathered}[/tex]So, the zeros are,
[tex]-1,3i,-3i[/tex]Final answer:
The zeros are,
[tex]-1,3i,-3i[/tex]