Question

Find the polynomial f(x) that has the roots of –3, 5 of multiplicity 2.

Answer 1

\[(x+3)^2(x-5)^2\]
Expand if required.

Answer 2

Is that (x+3)^2 times (x-5)^2

Answer 3

yes

Answer 4

It expands to
\[x^4-4\cdot x^3-26\cdot x^2+60\cdot x+225\]

Answer 5

you mean like: x^4-4x^3-26x^2+60x+225

Answer 6

yes

Answer 7

are they both multiplicity of two?

Answer 8

if not then that solution is not correct

Answer 9

Uh the way its phrased it suggests that both are of multiplicity 2.

Answer 10

I took it as only being the 5, bit confusing, I think.

Answer 11

Fine, if only root 5 is of multiplicity 2 then:
\[(x + 3)\cdot(x - 5)^2\]
Expand as necessary.

Answer 12

You get:
\[x^3-7x^2-5x+75\]