Asked by Ryan
Find a third-degree polynomial equation with rational coefficients that has roots -1 and i+1
Answers
Answered by
Steve
if 1+i is a root, so is 1-i. So, the factors are
(x+1)(x-(1+i))(x-(1-i))
(x+1)((x-1)^2 - i^2)
(x+1)(x^2-2x+2)
x^3-x^2+2
(x+1)(x-(1+i))(x-(1-i))
(x+1)((x-1)^2 - i^2)
(x+1)(x^2-2x+2)
x^3-x^2+2
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