SOLUTION: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 5; zeros: 9, -i, -8+i

Algebra ->  Functions -> SOLUTION: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 5; zeros: 9, -i, -8+i       Log On


   

Question 757294: Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 5; zeros: 9, -i, -8+i
Found 2 solutions by stanbon, tommyt3rd:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 5; zeros: 9, -i, -8+i
-----
f(x) = (x-9)(x+i)(x-i)(x+8 - i)(x+8 +i)
----
= (x-9)(x^2+1)((x+8)^2+1)
----
= (x-9)(x^2+1)(x^2 + 16x + 65)
------------
etc.
Cheers,
Stan h.
================

Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
The general polynomial with these roots is:
%0D%0Ap%28x%29=a%28x-9%29%28x%2Bi%29%28x-i%29%28x-%28-8-i%29%29%28x-%28-8%2Bi%29%29%0D%0A

let a=1, then

%0D%0Ap%28x%29=%28x-9%29%28x%5E2%2B1%29%28x%5E2%2B16x%2B65%29%0D%0A


%0D%0Ap%28x%29=x%5E5%2B7x%5E4-78+x%5E3-578+x%5E2-79+x-585%0D%0A

:)