- #1
DryRun
Gold Member
- 838
- 4
Homework Statement
Given 2 + 3i is one root of the equation:
x^4 - 6x^3 + 26x^2 -46x +65 = 0
Find the remaining roots.
The attempt at a solution
I am thinking about this as a possible solution although it is too long to be plausible, unless I'm wrong.
let x = a + bi and then replace in the polynomial. Then, expand and finally, divide it by 2+3i
Another possibility (i'm not sure) is this:
x (x^3 - 6x^2 + 26x -46) +65 = 0
So, i try to solve the cubic equation: x^3 - 6x^2 + 26x -46
However, note that one solution to x, is not equal to -65. So, this method is wrong, i believe.
I frankly don't know how else to go about to solve this one.
Given 2 + 3i is one root of the equation:
x^4 - 6x^3 + 26x^2 -46x +65 = 0
Find the remaining roots.
The attempt at a solution
I am thinking about this as a possible solution although it is too long to be plausible, unless I'm wrong.
let x = a + bi and then replace in the polynomial. Then, expand and finally, divide it by 2+3i
Another possibility (i'm not sure) is this:
x (x^3 - 6x^2 + 26x -46) +65 = 0
So, i try to solve the cubic equation: x^3 - 6x^2 + 26x -46
However, note that one solution to x, is not equal to -65. So, this method is wrong, i believe.
I frankly don't know how else to go about to solve this one.