I have to get the null-point(s) of a curve/function. The original function goes like this:

(i tried to use the MATH BBCode tags but I don't know how to use them so they caused errors)

f(x) = -x⁴ / 2 + 2x²

To get the null-points (not sure if it's called that in English) I have to set the above to be equal to zero:

-x⁴ / 2 + 2x² = 0

Next, I do ×2 on the equation:

-x⁴ + 4x² = 0

Then I say thatx² = uso that I can use a formula later

-u² + 4u = 0

Now I use this formula to get u₁ and u₂

(I think it's fromVieta)

x² + px + q = 0

₁x₂ = -p / 2 ± √((p / 2)² - q)

In my equation I don't have aqso I don't know if that conflicts with the proper use of the formula. Anyway, I went on to replace the variables in the formula with the ones from my equation (leaving out the- qpart inside the square-root section):

₁u₂ = -2 ± √4

That leaves me with these results for ₁u₂

u₁ = 0

u₂ = -4

Sinceuis actuallyx²we get ₁x₂ from the square-root of u₁

x₁ = 0

x₂ = 0

Now my first question is if the above is correct.Isx₂ zero as well, if u₁ was zero? ( ₁x₂ = ±√u₁ )

Next, I'd do the same with u₂ but since u₂ is -4 and you can't get the square-root of negative numbers (without resorting to Complex Numbers) this leaves me with no answer to x₃ and x₄

Is this true, or what am I doing/understanding wrong?

Please help me out quickly, I need this homework done today!

Thanks so much!!