Find a polynomial P(x) having real coefficients, with the degree and zeroes indicated. Assume the lead coefficient is 1.

Question

Find a polynomial P(x) having real coefficients, with the degree and zeroes indicated. Assume the lead coefficient is 1.

Recall:

degree 4, x = −1, x = 3 x − 2i

Answer 1

zeros: -1, 3, 2i, -2i

factors with opposite signs

(x+1)(x-3)(x-2i)(x+2i)

= (x^2 -2x -3)(x^2 +4)

= x^4 -2x^3 +x^2 -8x -12