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

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


   

Question 756890: Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 5; zeros: 9, -i, -8+i
F(x)=a_______
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Just some help but no further:

The needed set of zeros is
{ 9, -i, +i, -8+i, -8-i }

The factored form is f%28x%29=%28x-9%29%28x-%28-i%29%29%28x-%28i%29%29%28x-%28-8%2Bi%29%29%28x-%28-8-i%29%29
You have some multiplications and simplifications to do. Avoid extra difficulties through careful pre-simplification and associating:
f%28x%29=%28x-9%29%28x%2Bi%29%28x-i%29%28x%2B8-i%29%28x%2B8%2Bi%29
f%28x%29=%28x-9%29%28x%2Bi%29%28x-i%29%28%28x%2B8%29-i%29%28%28x%2B8%29%2Bi%29
Continue the multiplications and simplifications.