Find a formula for the polynomial P(x)

Question

Find a formula for the polynomial P(x) with, degree 3, real coefficients, zeros at x= -i and x=1, leading coefficient of a=1

Answer 1

A degree three polynomial has three roots.  All imaginary roots must come in pairs, so if x=-i is a root then x=i is also a root.  The three roots lead to 3 factors  (x- (-i))(x - i) and (x - 1), so the polynomial is:

 

P(x) = (x + i)(x - i)(x - 1) = (x² + 1)(x - 1)= x³ - x² + x - 1