Question

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

$f\left(x\right)=x^4+2x^3+22x^2+50x-75$

Short answer

The complex roots of the polynomial is$5i,-5i$

Step-by-step solution

Given information

We are given a polynomial$f\left(x\right)=x^4+2x^3+22x^2+50x-75$

Factor the polynomial

We get,

$$\begin{gathered} x^4+2x^3+22x^2+50x-75=0 \\ {x}^4+2x^3-3x^2+25x^2+50x-75=0 \\ {x}^2(x^2+2x-3)+25(x^2+2x-3)=0 \\ (x^2+25)(x^2+2x-3)=0 \\ (x-5i)(x+5i)(x+3)(x-1)=0 \end{gathered}$$

Conclusion

The complex roots of the polynomial are$5i,-5i$