SOLUTION: Hi, I have to find a 5th degree polynomial with real coefficients whose zeros are 0, 0, 0, i. I've completed problems like this before but I've never seen zeros of 0, not sure

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi, I have to find a 5th degree polynomial with real coefficients whose zeros are 0, 0, 0, i. I've completed problems like this before but I've never seen zeros of 0, not sure       Log On


   

Question 367446: Hi, I have to find a 5th degree polynomial with real coefficients whose zeros are 0, 0, 0, i.
I've completed problems like this before but I've never seen zeros of 0, not sure how to start with this one. If you could just direct me how to set this problem up, I should be good to go.
Thanks so much!

Found 2 solutions by edjones, scott8148:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x=0, x=0, x=0, x=i, x=-i
(x-0)^3(x-i)(x+i)
=x^3(x-i)(x+i)
=x^3(x^2+1)
=x^5+x^3
.
Ed

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
if r is a root (zero) of a polynomial , then x-r is a factor

complex roots (like i) occur in conjugate pairs ___ if i is a root , so is -i

the factors of your polynomial are ___ (x - 0)(x - 0)(x - 0)(x + i)(x - i)