Question

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. Degree 3; zeros: -9, 9- i

Answer 1

Using the Complex Conjugate Root Theorem, we know that if a complex number a+bi is a root of a complex polynomial with real coefficients, then a-bi, the complex conjugate of a+bi, is also a root.

Since -9 and 9-i are roots of f, and -9 is a real number, then the remaining zero of the function must be the complex conjugate of 9-i:

$9+i$