Question

Find the polynomial f(x) that has the roots of -2, 3 of multiplicity 2. Explain how you would verify the zeros of f(x)

Answer 1

Root of 'a' implies factor of (x-a). Go!

Answer 2

could you explain more?

Answer 3

Root of 3 implies factor of (x-3).

Answer 4

so would it only be (x+2)(x-3)

Answer 5

Excellent, excepting the word "multiplicity", What shall we do with that?

Answer 6

multiply both sides by 2 ?

Answer 7

Good guess, but you've only one side. Just repeat yourself.

Root of 3 implies factor of (x-3)

Root of 3 multiplicity 2 implies factor of (x-3) twice, either (x-3)(x-3) or more simply \((x-3)^{2}\)

Answer 8

ooh okok once i get the exponent on both sides what do i do ?? so i just multiply -3 *-3?

Answer 9

Where are you getting the "both sides"? We are creating an algebraic expression. There's only one side. Let's try this.

Give these zeros, create a polynomial with these zeros.

-2
3

(x+2)(x-3)

Give these zeros, create a polynomial with these zeros.

-2
3
3

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

Give these zeros, create a polynomial with these zeros.

-2
3 (multiplicity 2)

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

Give these zeros, create a polynomial with these zeros.

-2
3 (multiplicity 5)

(x+2)(x-3)^5