Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

7, -11, and 2 + 8i

Answer 1

A polynomial with real coefficients has real roots or complex roots or a combination of both, but if it does have complex roots, the complex roots must be in complex conjugate pairs.

Since you have the root 2 + 8i, you must also have the root 2 - 8i.

That means you have the roots 7, -11, 2 + 8i, and 2 - 8i.

Ok so far?

Answer 2

To find the polynomial that has roots a, b, c, and d, multiply this together:

(x - a)(x - b)(x - c)(x - d)