SOLUTION: given that f(x) is a cubic function with zeros at -5 and -4i +3, find an equation for f(x) given that F(8)=2 .

Algebra ->  Expressions-with-variables -> SOLUTION: given that f(x) is a cubic function with zeros at -5 and -4i +3, find an equation for f(x) given that F(8)=2 .      Log On


   

Question 1060861: given that f(x) is a cubic function with zeros at -5 and -4i +3, find an equation for f(x) given that F(8)=2 .
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=k%28x%2B5%29%28x-%283-4i%29%29%28x-%283%2B4i%29%29
f%28x%29=k%28x%2B5%29%28%28x-3%29%2B4i%29%28%28x-3%29-4i%29
f%28x%29=k%28x%2B5%29%28x%5E2-6x%2B9-16i%5E2%29
f%28x%29=k%28x%2B5%29%28x%5E2-6x%2B9-16%29
f%28x%29=k%28x%2B5%29%28x%5E2-6x-7%29

You want to use the given point to help solve for and evaluate k.
k%288%2B5%29%288%5E2-6%2A8-7%29=2
What is k?

Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
.
f(x) = k%28x%2B5%29%28x-%283-4i%29%29%28x-%283%2B4i%29%29

f(x) = k%28x%2B5%29%28%28x-3%29%2B4i%29%28%28x-3%29-4i%29

f(x) = k%28x%2B5%29%28x%5E2-6x%2B9-16i%5E2%29

f(x) = k%28x%2B5%29%28x%5E2-6x%2B9%2B16%29

f(x) = k%28x%2B5%29%28x%5E2-6x%2B25%29


Use the given condition f(8)=2 to find k.

k%2A%288%2B5%29%2A%288%5E2-6%2A8%2B25%29 = 2.

k = 2%2F%2813%2A41%29 = 2%2F533.

f(x) = %282%2F533%29%2A%28x%2B5%29%2A%28x%5E2-6x%2B25%29.