Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
4, -14, and 5 + 8i

f(x) = x4 - 362.5x2 + 1450x - 4984
f(x) = x4 - 9x3 + 32x2 - 725x + 4984
f(x) = x4 - 67x2 + 1450x - 4984
f(x) = x4 - 9x3 - 32x2 + 725x - 4984

Answer 1

@jim_thompson5910 do you mind helping out again?

Answer 2

if 5 + 8i is a root, then


x = 5 + 8i
x - 5 = 8i
(x - 5)^2 = (8i)^2
(x - 5)^2 = 64i^2
(x - 5)^2 = 64(-1)
(x - 5)^2 = -64
x^2 - 10x + 25 = -64
x^2 - 10x + 25+64 = -64+64
x^2 - 10x + 89 = 0


So if 5 + 8i is a root, then x^2 - 10x + 89 is a factor.


Take a few minutes to review this over. If you have any questions so far, then let me know. If not, then tell me when you're ready for the next step.