# Thread: Roots of a polynomial equation

1. ## Roots of a polynomial equation

I'm pretty lost here.. and simply unclear on what exactly I should be doing.
If someone could walk me through the steps to getting this answer, I'd extremely appreciate it.

Find the roots of the polynomial equation: $\displaystyle x^3 - 4x^2 + 6x - 4 = 0.$

I've used synthetic division to find -2 as a root and get the depressed polynomial $\displaystyle x^2 - 2x + 2$.. and then used the quadratic formula to find what I think are the correct zeroes of that equation. (which are: 1+i, 1-i.)

Here's where I'm unsure of what to do. Thanks for your help!

2. Originally Posted by Savior_Self
I've used synthetic division to find -2 as a root and get the depressed polynomial $\displaystyle x^2 - 2x + 2$.. and then used the quadratic formula to find what I think are the correct zeroes of that equation. (which are: 1+i, 1-i.)
Well done!

3. Originally Posted by Savior_Self
I'm pretty lost here.. and simply unclear on what exactly I should be doing.
If someone could walk me through the steps to getting this answer, I'd extremely appreciate it.

Find the roots of the polynomial equation: $\displaystyle x^3 - 4x^2 + 6x - 4 = 0.$

I've used synthetic division to find -2 as a root and get the depressed polynomial $\displaystyle x^2 - 2x + 2$.. and then used the quadratic formula to find what I think are the correct zeroes of that equation. (which are: 1+i, 1-i.)

Here's where I'm unsure of what to do. Thanks for your help!
Hi Savior_Self,

-2 is not one of your roots. (x - 2) is a factor of your original cubic function, but the root is +2.