- #1

fishturtle1

- 394

- 82

## Homework Statement

Solve for the roots of the following.

(What do you notice about the complex roots?)

b) x

^{3}+ x

^{2}+ 2x + 1 = 0

## Homework Equations

To find roots of a polynomial of degree n > 3, look at the constant and take all its factors. Those are possible roots. Then plug them into see which ones solve the equation.

cubic equations from this link: http://www.mathportal.org/formulas/algebra/solalgebric.php

## The Attempt at a Solution

factors of 1: 1, -1

x=1

(1)

^{3}+ 1

^{2}+ 2(1) + 1 = 0

1 + 1 + 2 + 1 = 0

5 = 0, so 1 is not a root.

x=-1

(-1)

^{3}+ (-1)

^{2}+ 2(-1) + 1 = 0

-1 + 1 -2 + 1 = 0 -> -1 = 0

So -1 is not a root.

I also tried to use cubic formulas and did not find the correct answer. I checked my calculations.

So i think there is some method more simple than cubic equations that I cannot think of/find on the web.

Are there any other ways besides testing the constant term's factors, and using the cubic equations, to find the roots of a 3rd degree polynomial?