Question

form a polynomial function f(x) with real coefficients having the given degree and zeros. Answers will vary depending on the choice of the leading coefficient. Use a graphing utility to graph the function and verify the result.

Degree 4; zeros: 3 multiplicity 2; -i

Short answer

The polynomial can be given as$f\left(x\right)=x^4-6x^3+10x^2-6x+9$

Step-by-step solution

Given information

We are given the degree of polynomial to be 4 the zeros are -i and 3 with multiplicity 2

Find the equation

As -i is one of the roots by conjugate properties we get i as one of the root of the polynomial

Hence

$$\begin{gathered} f\left(x\right)=(x-i)(x+i)(x-3)(x-3) \\ f\left(x\right)=(x^2+1)(x^2-6x+9) \\ f\left(x\right)=x^4-6x^3+10x^2-6x+9 \end{gathered}$$

Conclusion

The polynomial can be given as$f\left(x\right)=x^4-6x^3+10x^2-6x+9$