anonymous
  • anonymous
Find a polynomial f(x) of degree 3 that has the following zeros: -9,2,0 Leave your answer in factored form.
Mathematics
katieb
  • katieb
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mathmate
  • mathmate
If a 3rd degree polynomial has three known roots x1,x2,x3, then the factored form is: a(x-x1)(x-x2)(x-x3)=0 where a is an arbitrary constant.
anonymous
  • anonymous
So in this case, x(x+9)(x-2) ?
phi
  • phi
remember, zeros mean when x= -9 , x= 2 and x=0 then the polynomial is 0 if you rearrange these 3 equations you get x+9=0 x-2=0 x=0 when you multiply them together you get x(x-2)(x+9) = (obviously) 0 you could also multiply by some number a, and it will still be 0 a x (x-2) (x+9) = 0

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phi
  • phi
for this question, leave a=1 for the simplest form. But you could pick any a you want (except a=0)
anonymous
  • anonymous
Thanks for the help.

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