Find an nth-degree polynomial function with real coefficients satisfying the given conditions.

Question

n=3

-2, 3+5i, 3-5i are the zeros

f(2) = 104

I can get the first part with x- each zero and then distributing them. Struggling with what to do with the f(2)=104.

Answer 1

Please show us the work you've done so far, so we can fill in the details. Especially, the zeroes from x = 3 +- 5i

Together the two complex zeroes should generate a quadratic factor which does not factor into real binomials.

As to the property, f(2) = 104, try applying the following.

Here's a hint: when x is a zero solution.

0 = M * ( a x² + bx + c )

Put in your numbers for a, b & c.

Then apply

104 = M * (a 2² + b* 2 + c )

Can you fill in the rest of the details?