Find a polynomial equation with real coefficients that has the given roots.

Question

Write a polynomial equation with roots 5 and -9i.

Answer

x^3-(answer goes here)x^2+(answer goes here)x-(answer goes here) = 0

Answer 1

The factors would be (x-5)(x+9i)(x+9i) For each complex zero, you also have to use the complex conjugate for another zero.

Now, multiply out. FOIL the last 2 factors.

(x-5)(x²+81)

FOIL again

x³-5x²+81x-405