Posted by **Emily** on Tuesday, December 8, 2009 at 11:56pm.

Solve the equation x^3 - 2x + 4 = 0.

==> I know the answer is -2, but I can't seem to remember how to solve these by hand without using a graphing calculator. Any help is greatly appreciated!! :)

- Precalculus -
**Reiny**, Wednesday, December 9, 2009 at 12:17am
Unless they factor, cubic equations cannot be easily solved "by hand"

In this case, try subbing ±1 and ±2 into the equation to get a zero.

You were right to find that x = -2 works

so (x+2) must be a factor.

Use long algebraic division or synthetic division to find the other factor to be (x^2 - 2x + 2)

using the quadratic formula on

x^2 - 2x + 2 = 0 gives me two complex roots, namely (1 ± i)/2

- correction - Precalculus -
**Reiny**, Wednesday, December 9, 2009 at 12:23am
the two complex roots should have been just

1 ± i

- Precalculus -
**Emily**, Wednesday, December 9, 2009 at 12:32am
Ohhh I see. Thanks Reiny this helped a lot!! :)

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