# Homework Help: X^3 - 4x^2 + 4x +2 = 0

1. Nov 23, 2012

### davon806

1. The problem statement, all variables and given/known data
Please see the method of solving the equation x^3 -4x^2 + 4x +2 = 0 from the attached.
In the red brackets,can anyone explain why the negative root is not involved in the calculation?
z = [y±√(y^2 - 4k)]/2
so why only y+√(y^2 - 4k) is considered?
and in the second bracket,again,why the another root of u ,(-1/27)(-35 - 3√129),is not used?
Both roots are negative.
Thx.
2. Relevant equations

3. The attempt at a solution

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2. Nov 23, 2012

### tiny-tim

hi davon806!
you can use the "negative" root in either or both cases, and it should give the same result in the end …

have you tried it?

3. Nov 24, 2012

### davon806

As there are 2 solutions of z and 2 solutions of u,
there are 4 possible answers for x
z = [y ± √(y^2 - 4k)]/2 , u = 1/27(-35 ± 3√129)
if both of the signs are +,or both signs are -,the value of x would be:
x = 4/3 - 4/[3(35-3√129)^(1/3) - 1/3(35-3√129)^(1/3)]
if z = [y+√(y^2 - 4k)]/2 and u = (-35-3√129)/27 ,
x = 4/3 - 4/[3(35+3√129)^(1/3) - 1/3(35+3√129)^(1/3)]

What's wrong?Thx.

4. Nov 24, 2012

### tiny-tim

hi davon806!
ah, but 1/(35-3√129) = (35+3√129)/64