Question

f(x) = x^3 + x^2 + 9x + 9find all zeros invluding irrational and/or complexfavtor f completely into linear factors

Answer 1

ANSWER :

The zeros are -1, 3i and -3i

EXPLANATION :

From the problem, we have :

$f(x)=x^3+x^2+9x+9$

Factor completely :

$\begin{gathered} f(x)=x^2(x+1)+9(x+1) \\ f(x)=(x^2+9)(x+1) \end{gathered}$

Zeros are values of x when f(x) = 0

That will be :

$0=(x^2+9)(x+1)$

Equate both factors to 0.

$\begin{gathered} x^2+9=0 \\ x^2=-9 \\ x=\sqrt{-9} \\ x=3i\quad and\quad x=-3i \end{gathered}$$\begin{gathered} x+1=0 \\ x=-1 \end{gathered}$