SOLUTION: Find a polynomial equation with real coefficients that has the given zeros. 1-2i and 1+2i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a polynomial equation with real coefficients that has the given zeros. 1-2i and 1+2i      Log On


   

Question 974749: Find a polynomial equation with real coefficients that has the given zeros.
1-2i and 1+2i
Answer by amarjeeth123(569) About Me  (Show Source):
You can put this solution on YOUR website!
The required equation is (x-1+2i)(x-1-2i)=0
x^2 - (1 - 2i)x - (1 + 2i)x + (1 - 2i)(1 + 2i)
= x^2 - x + 2ix - x - 2ix + (1 + 2i - 2i - 4i^2)
= x^2 - 2x + 1 - 4i^2
= x^2 - 2x + 1 + 4
= x^2 - 2x + 5
The required equation is x^2-2x+5=0