(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

y^4 + 3y^2 - 4 = 0

2. Relevant equations

3. The attempt at a solution

The base, I know, is y^2. So in order to make this a quadratic equation, we come up with an arbitrary variable, say α, which is equal to the base. Re-writing this, we get:

(y^2)^2 + 3(y^2) - 4 = 0

α = y^2

α^2 + 3α - 4 = 0

So now it's a quadratic equation.

Factoring, we get:

(α - 1) (α + 4) = 0

Setting both of these equal to zero, we get:

α = 1 and α = -4

This next part is where I'm lost, so maybe one of you bright people can show me where I'm making my mistake.

We start with α = -4.

Since α = y^2, -4 must = y^2 too.

-4 = y^2

Solving this for y, we get:

y = sqrt(-4) = 2i.

However, in the text - without any explanation as to how this occurs (which is what is confusing me about these problems) - it says that the two solutions are 2i and -2i.

Can someone please explain this step to me. D:

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Equations Quadratic in Form ;_;

**Physics Forums | Science Articles, Homework Help, Discussion**