Question

Part 1: Find the polynomial f(x) that has the roots of –2, 3 of multiplicity 2. (4 points)

Part 2: Explain how you would verify the zeros of f(x). (4 points)

Answer 1

A polynomial having two roots can be written as
\[(x-a)^p(x-b)^q\]

where
a-->first root
b-->second root.
p-->multiplicity of root a
q-->multiplicity of root b

Given p=1 and q=2

and the roots are a=–2, b= 3

Can you substitute and simplify the polynomial now??

Answer 2

For part 2:
After you get the polynomial from the part 1. Substitute
1) x = -2 you will get the polynomial value as 0
2)Similarly substitue the second root in place of x and you should get polynomial value as 0

In case of any doubt, post it here :)

Answer 3

Okay thank you

Answer 4

Welcome :)