SOLUTION: nth degree polynomial function w/real coefficients satisfying the given conditions n=3 -3 and 1+5i are 0 f(2)=130 f(x)=

Question 972920: nth degree polynomial function w/real coefficients satisfying the given conditions
n=3
-3 and 1+5i are 0
f(2)=130
f(x)=
Found 2 solutions by josgarithmetic, KMST:
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
-3 and 1+5i ARE ZEROS.
This must also include 1-5i.

Start with , and simplify into general form, but keep the unknown factor k, UNDISTRIBUTED.

Next step from the raw factored form,

and then

Keep going...
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
A polynomial function of degree has complex zeros.
If a polynomial function w/real coefficients has a non-real complex zero,
then the conjugate complex number is also a zero.
Then, the complex zeros of are , , and .
So the factored form of is

So, -->-->-->--> .
So, in factored form,
and if that's not the required form, we can multiply and get

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