Find a polynomial with integer coefficients that satisfies the given conditions.

Question

R has degree 4 and zeros 5 − 5i and 1, with 1 a zero of multiplicity 2.

Answer 1

x=5-5i

x-5=5i

x^2-10x+25=-25

x^2-10x+50=0

R=(x^2-10x+50)(x-1)^2

=(x^2-10x+50)(x^2-2x+1)

=x^4 -12x^3 +31x^2 -110x +50