SOLUTION: n=3, 4 and 5 i are zeros; f(-1) = 260 find the answer in polynomial form. thank you

Algebra ->  Rational-functions -> SOLUTION: n=3, 4 and 5 i are zeros; f(-1) = 260 find the answer in polynomial form. thank you      Log On


   

Question 956247: n=3, 4 and 5 i are zeros;
f(-1) = 260
find the answer in polynomial form. thank you
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
n=3, 4 and 5i are zeros;
f%28-1%29+=+260

f%28x%29=%28x-3%29%28x-4%29%28x-5i%29....multiply all and you will get
f%28x%29=x%5E3-7x%5E2%2B%28-5x%5E2%2B35x-60%29%2Ai%2B12x+
to get f%28-1%29+=+260, we need to find some constant k to multiply x%5E3-7x%5E2%2B%28-5x%5E2%2B35x-60%29%2Ai%2B12x+ for x=-1 to get 260
%28%28-1%29%5E3-7%28-1%29%5E2%2Bi%28-5%28-1%29%5E2%2B35%28-1%29-60%29%2B12%28-1%29+%29k=+260
%28-1-7%2Bi%28-5-35-60%29-12+%29k=+260
:
:
k+=+-1%2F2%2B%285i%29%2F2
then we have
f%28x%29=%28x%5E3-7x%5E2%2Bi%28-5x%5E2%2B35x-60%29%2B12x%29%28-1%2F2%2B%285i%29%2F2%29