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F(x) = x^3 + x^2 + 9x + 9 Find all zeros including irrational and/ or complexFactor f completely into linear factors Part of it completed: The zeros are -1, 3i, and -3i

Sagot :

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]
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