Question

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

$f\left(x\right)=x^4+5x^2+4$

Short answer

The zeros of the polynomial are$2i,-2i,i,-i$

Step-by-step solution

Given information

We are given a polynomial$f\left(x\right)=x^4+5x^2+4$

Find the zeros

We get,

$$\begin{gathered} x^4+5x^2+4=0 \\ (x^2+4)(x^2+1)=0 \\ (x-2i)(x+2i)(x-i)(x+i)=0 \end{gathered}$$

Conclusion

The zeros of the polynomial is$2i,-2i,i,-i$