Find a polynomial function of least degree having only real

Find a polynomial function of least degree having only real coefficients with zeros 0, I, and 1+i.

Solution

zeros are 0 , 1

complex zero = 1+i

It would also have complex conjugate zero = 1-i

Polynomial would atleast have f(x) = a(x)(x-1)(x -1 -i)(x - 1 +i)

= a*x(x-1)(x^2 -x +i*x - x +1 -i -ix +i +1)

f(x) =a*x(x-1)(x^2 - 2x +2) where \'a\' is a constant