SOLUTION: Given that 2i and 3i are both roots of the equation z˄6 + z˄5 + 11z˄4 + 13z˄3 + 10z˄2 + 36z - 72. Factorize in terms of real factors.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Given that 2i and 3i are both roots of the equation z˄6 + z˄5 + 11z˄4 + 13z˄3 + 10z˄2 + 36z - 72. Factorize in terms of real factors.      Log On


   

Question 1123378: Given that 2i and 3i are both roots of the equation z˄6 + z˄5 + 11z˄4 + 13z˄3 + 10z˄2 + 36z - 72.
Factorize in terms of real factors.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
factors are (x-2i)(x+2i) and (x-3i) and (x+3i) (I will use x not z)
The first expands to x^2+4 and the second to x^2+9
They expand to x^4+13x^2+36
Use polynomial division dividing into the equation.
This will give (x^2-x-2) with no remainder, or (x-2)(x-1) ANSWER