SOLUTION: Hello, I have a test tomorrow in Algebra, and I am struggling with finding a third degree polynomial equation from it's roots. The given roots are 1, 2-i, and I know that 2 + i

Question 613866: Hello, I have a test tomorrow in Algebra, and I am struggling with finding a third degree polynomial equation from it's roots.
The given roots are 1, 2-i, and I know that 2 + i is also a root because it is a complex conjugate. I"ve factored the polynomial, but I am having trouble multiplying the factors, because the imaginary numbers are making it very complex for me
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
multiply the imaginaries 1st, the +- i terms will mostly cancel

(x - 2 + i)(x - 2 - i) = x^2 - 4x + 4 - i^2 = x^2 - 4x + 5

(x - 1)(x^2 - 4x + 5) = x^3 - 4x^2 + 5x - x^2 + 4x - 5 = x^3 - 5x^2 + 9x - 5
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