Nth-degree polynomial

Question

Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n=3; 4 & 5i are zeros; f (-1)=130 f(x)=??? (type a polynomial in standard form)

Answer 1

The complex conjugate of a complex zero must also be a zero, so your 3 zeros are

4

5i

-5i

f(x) = A(x - 4)(x - 5i)(x + 5i) = A(x - 4)(x² + 25)

130 = A(-1 - 4)[(-1)² + 25]

130 = -5A(26) = -130A

A = -1

f(x) = -(x - 4)(x² + 25)

You should be able to expand this to standard form and finish from here.