Question 61715
Find all three zeros of f(x)=x^3-4X^2+13x+50 given that 3+4i is a zero 
:
Find the expression for 3 + 4i, reverse the procedure of completing the square:
x = 3 + 4i
x - 3 = 4i
:
Square both sides
(x-3)^2 = 4i * 4i
:
x^2 - 6x + 9 = 16(i^2)
:
Remember i^2 = -1
x^2 - 6x + 9 = 16(-1)
x^2 - 6x + 9 = -16
x^2 - 6x + 9 + 16 = 0
x^2 - 6x + 25 = 0 
:
We can see that the last term is 50 so the above expression has to multiplied by the factor (x + 2) to get x^3 - 4X^2 + 13x + 50
:
The 3 zeros: -2, 3+4i, 3-4i