Find a polynomial with integer coefficients that satisfies t

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

P has degree 2 and zeros 1 + i sqrt(7) and 1 - i sqrt(7)

Solution

P has degree 2 and zeros 1 + i7 and 1 - i7

P(x)=(x-(1+i7))(x-(1-i7))

P(x)=(x-1 -i7))(x-1+ i7))

P(x)=(x-1)²-(i7)²

P(x)=(x²-2x+1)-(-49)

P(x)=x²-2x+50