Find a third-degree polynomial equation with rational coefficients that has the given numbers as roots. -5 and 1 - i

Braxton Pugh 2020-12-29 Answered
Find a third-degree polynomial equation with rational coefficients that has the given numbers as roots. -5 and 1 - i
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Expert Answer

Raheem Donnelly
Answered 2020-12-30 Author has 75 answers

if1-i is a root, so its complex conjugate, 1+i. Write factors (xk) where k is a root for all 3 roots. Then multiply together.
(x(5))(x(1i))(x(1+i))=(x+5)(x2x(1+i)x(1i)+1(1i)(1+i))
=(x+5)(x2xixx+ix+1ii2)
=(x+5)(x22x+2)
=x32x2+2x+5x210x+10
=x3+3x28x+10

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