Find a degree 3 polynomial with real coefficients having zeros 3 and 3i and a lead coefficient of 1. Write in expanded from.

Answer 1

If a 3 degree polynomial has a zero of 3i, it also has a zero of -3i. They come in conjugate pairs, if the polynomial has all real coefficients

take 3, 3i and -3i and change their signs, then add to x to get 3 factors, x-3, x-3i, and x--3i=x+3i

(x-3)(x-3i)(x+3i) Now multiply them together to get the polynomial with coefficient 1

=(x-3)(x²+9)

=x³ -3x² +3=9x-27