Third-degree, with zeros of 3−i, 3+i, and 4, and a leading coefficient of −6.

Question

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.

Third-degree, with zeros of 3−i, 3+i, and 4, and a leading coefficient of −6.

Answer 1

I will set up the solution for you, but YOU do the work. You have the 3 zeros and the leading coefficient, so

f(x) = -6 [x - (3 - i)] [x - (3 + i)] (x - 4)

Expand f(x) and simplify. All the coefficients will come out real.