- #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.