SOLUTION: Hi, How do you solve: x^3 - 2x^2 + 9x - 18 = 0 the teacher has given us one solution, 3i/square root of -9. i need two other solutions and am not sure how to obtain them

Algebra ->  Radicals -> SOLUTION: Hi, How do you solve: x^3 - 2x^2 + 9x - 18 = 0 the teacher has given us one solution, 3i/square root of -9. i need two other solutions and am not sure how to obtain them      Log On


   

Question 344326: Hi,
How do you solve: x^3 - 2x^2 + 9x - 18 = 0
the teacher has given us one solution, 3i/square root of -9.
i need two other solutions and am not sure how to obtain them.
i have tried rational root theorem/ long division but do not know how to do it with square roots and imaginary numbers.
thanks
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complex solutions always come in complex conjugate pairs.
So, if 3i is a solution, then -3i is also a solution.
%28x-3i%29%28x%2B3i%29=x%5E2%2B9
You can then use polynomial long division to find the last root,
You can then get %28x%5E3-2x%5E2%2B9x-18%29%2F%28x%5E2%2B9%29
Also, since only one root remains you know it must be real.
You could graph the equation and find it that way too.
.
.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3-2x%5E2%2B9x-18%29
.
.
Looks like x=2 might be a number to stick in the function to see if f%282%29=0.