Question

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

$f\left(x\right)=x^4+3x^3-19x^2+27x-252$

Short answer

The complex roots of the polynomial is$3i,-3i$

Step-by-step solution

Given information

We are given a polynomial

$f\left(x\right)=x^4+3x^3-19x^2+27x-252$

Factor the polynomial

We have,

$$\begin{gathered} x^4+3x^3-19x^2+27x-252=0 \\ (x^2+9)(x+7)(x-4)=0 \\ (x-3i)(x+3i)(x+7)(x-4)=0 \end{gathered}$$

Conclusion

The complex roots of the polynomial is$3i,-3i$