Find the general form of all real polynomials of least degree which have zeros 2 + i and - 1 + 3i

The coefficients must be real so each complex root must have a conjugate: 2-i and - 1-3i.

The factorisation is (x-2-i) (x-2+i) (x+1-3i) (x+1+3i) = (x²-4x+5) (x²+2x+10).

Expanded this is:

x⁴+2x³+10x²

-4x³-8x²-40x

+5x²+10x+50=

x⁴-2x³+7x²-30x+50.