Question

find the complex zeros of each polynomial function. Write f in factored form.

$f\left(x\right)=x^4+13x^2+36$

Short answer

The roots of the given polynomial$3i,-3i,2i,-2i$

Step-by-step solution

Given information

We are given a polynomial$f\left(x\right)=x^4+13x^2+36$

Factor the given polynomial

We get,

$$\begin{gathered} x^4+13x^2+36=0 \\ (x^2+9)(x^2+4)=0 \\ (x-3i)(x+3i)(x-2i)(x+2i)=0 \end{gathered}$$

Conclusion

The roots of the given polynomial is$3i,-3i,2i,-2i$