Question

Find all real zeros of the polynomial f(x)=x^4 + 8x^3 + 7x^2 and determine the multiplicity of each.
Help guys!

Answer 1

Factor out x^2 to get x^2(x^2+8x+7)
Factor further to get x^2(x+7)(x+1)
So we got 0 twice, -7 once, and -1 once

Answer 2

okay, would the multiplicties be 2, 1, and 1?

Answer 3

@FutureMathProfessor

Answer 4

Yes

Answer 5

okay, thanks. can you help me with another one?
Find a plynomial with the given zeros. -1, 7, -√2, √2. We have to expand the expression too.

Answer 6

Your polynomial is (x+1)(x-7)(x+sqrt2)(x-sqrt2)
Just do foil three times.

Answer 7

How do I do it with the square roots? I can get it until I have to start adding and subtracting them..

Answer 8

wait.. nevermind. I figured it out.