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

A polynomial function that has roots a, b, c, d has equation:
(x - a)(x - b)(x - c)(x - d) = 0

Answer 2

Also, if a polynomial function with real coefficients has complex roots, then the complex roots come in complex conjugate pairs.

Answer 3

so which one is it?

Answer 4

I don't know. You need to write it out and multiply it out. I can;t guess it from just looking.

Answer 5

You are given roots 4 and -14.
Then you are given root 5 + 8i. Since 5 + 8i is complex, and the coefficients of the polynomial are real, you must also have root 5 - 8i.

Answer 6

You need to multiply this out:
\(\large (x - 4)[x - (-14)][x - (5 + 8i)][x - (5 - 8i)] = 0\)

Answer 7

First simplify each factor:
\(\large (x - 4)(x + 14)(x - 5 - 8i)(x - 5 + 8i) = 0\)

Answer 8

thanks i got the answer it was c