Question

PLEASE HELPP!!

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)

Is there a certain formula i would use, or?
I don't get how to solve the question.

Answer 1

no, you just need to know is that if x = a is a root then (x - a) is a factor.

multiplicity means the number of times the root or factor is repeated

as an example (x - 5)^2 = 0 has a repeated root at x = 5 so has multiplicity 2.

so looking at your question the factors are including multiplicity

f(x) = (x +2)(x -3)^2

you now need to distribute

Answer 2

Thank you, Now how would i verify the zeros? To answer the next part??

Answer 3

I would assume by using Descartes' Rule of Signs?

Answer 4

the easy way to verify the zeros is substitution

substitute x = -2 and it should be equal to zero

same for x = 3

this is called the factor theorem.