1. Explain how to determine the equation of the function with the following zeros. Be sure to explain each step as you show
how to determine the equation.
-5 multiplicity 2
-2 multiplicity 1

Step-by-step explanation:

Roots of a polynomial

If we know the roots of a polynomial, say x1,x2,x3,...,xn, we can construct the polynomial using the formula

Where a is an arbitrary constant.

We are given the following roots:

-5 multiplicity 2 (-5 twice)

-2 multiplicity 1

Thus, the polynomial is:

We are not given any clue about the value of a, so we choose a=1. Multiplying:

Simplifying:

correct answer:

i^31 = -i