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## Homework Statement

p(x) = x^3 − x^2 + ax + b is a real polynomial with 1 + i as a zero, find a and b and find all of the real zeros of p(x).

## The Attempt at a Solution

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1-i is also a zero as it is the conjugate of 1+i

so

(x-(1+i))(x-(1-i))=x^2-2x+2

let X^3-x^2+ax+b=x^2-2x+2(ax+d)

constant terms: b=2d, d=b/2

x terms: -2d+2a, a=2d

This is what I have done so far but I am unsure how to find a and b and the third zero

Any Help would be appreciated