Question

Find a polynomial function P(x) if least degree with zeroes 7 and -2i. Write your final answer in expanded form complete with function name P(x).

Answer 1

1)  Polynomial with complex coefficients wil be

$P(x)=(x-7)(x-(-2i))=(x-7)(x+2i)=x^2+2ix-7x-14i=\\ \\=x^2+(2i-7)x-14i.$

2) Polynomial with real coefficients will be

$P(x)=(x-7)(x-(-2i))(x-2i)=(x-7)(x+2i)(x-2i)=(x-7)(x^2-(2i)^2)=\\ \\=(x-7)(x^2-4i^2)=(x-7)(x^2+4)=x^3-7x^2+4x-28.$