SOLUTION: find an expression in simplest form for a polynomial of third degree with real coefficients having roots of 3 and 1-2i

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: find an expression in simplest form for a polynomial of third degree with real coefficients having roots of 3 and 1-2i      Log On


   

Question 357132: find an expression in simplest form for a polynomial of third degree with real coefficients having roots of 3 and 1-2i
Answer by user_dude2008(1862) About Me  (Show Source):
You can put this solution on YOUR website!
(x-3)(x-(1-2i))(x-(1+2i))=0

(x-3)(x-1+2i)(x-1-2i)=0

(x-3)((x-1)+2i)((x-1)-2i)=0

(x-3)((x-1)^2+4)=0

x(x-1)^2+4x-3(x-1)^2-12=0

x(x^2-2x+1)+4x-3(x^2-2x+1)-12=0

x^3-2x^2+x+4x-3x^2+6x-3-12=0

x^3-5x^2+11x-15=0


Answer: x^3-5x^2+11x-15