Use the Factor Theorem to determine a polynomial equation, of lowest degree, that has only the indicated roots:
0 is a root of multiplicity 5, 2 is a double root

Question

Use the Factor Theorem to determine a polynomial equation, of lowest degree, that has only the indicated roots:
0 is a root of multiplicity 5, 2 is a double root

mertsj · Answer

x^5(x-2)^2=0

anonymous · Answer

ok i cant read. start with $$x^5(x-2)^2$$ and multiply out

anonymous · Answer

so I would get $$x ^{5}+x ^{2}-4x+4$$

anonymous · Answer

no i don't think so

anonymous · Answer

$$x^5(x-2)^2=x^5(x-2)(x-2)=...$$

anonymous · Answer

where does the extra (x-2)^2 come from then that you have after the x^5?

anonymous · Answer

oh nvm.... so what am I multiplying out then? the (x-2)^2 or?

mertsj · Answer

$$x^5(x-)(x-2)=x^5(x^2-4x+4)=x^7-4x^6+4x^5$$

anonymous · Answer

Oh ok so I just needed to continue multiplying to completly get rid of the parenthisis cool thank you...

so what if it is the same question but it says 1/3 is a double root and -2 is a double root? do I set it up like this:
f(x)=(x-1/3)^2(x+2)^2

mertsj · Answer

Yes

anonymous · Answer

awesome thanks so much for the help!

mertsj · Answer

yw

anonymous · Answer

Uh so I actually have one more silly question how do I get rid of the fraction to make that problem easier?

anonymous · Answer

NVM I figured it out:) thanks

anonymous · Answer

i wouldn't

anonymous · Answer

oh looks like you got it right? start with $(3x-1)^2$

anonymous · Answer

Thanks:)