find the polynomial equation of lowest degree and with integral coefficients for which the given numbers are r

Question

find the polynomial equation of lowest degree and with integral coefficients for which the given numbers are roots.

- (1+i)2

can you help me solve this math analysis problem?

Answer 1

There is no such polynomial. That's because
if a+bi is a root of a polynomial with integral
coefficients, a-bi is also a root.
To have -(1+i)/2 as a double root, the
polynomial would have to have complex coefficients.