Find a cubic polynomial with real coefficients

Question

Find a cubic polynomial with real coefficients having roots x=-2 and x=1+4i Assume a lead coefficient of 1.

Answer 1

x - 4i must also be a root.

 

P(x) = 1(x + 2)[x - (1 + 4i)][x - (1 - 4i)]

 

Go ahead and expand this.  The coefficients will come out real.