1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Equations Quadratic in Form ;_;

  1. Dec 25, 2011 #1
    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:
  2. jcsd
  3. Dec 25, 2011 #2
    Oh. Wait. I think I figured it out. When you take the square root of something we have to remember to put plus/minus, right? ;_; Maybe it's time to go back to radical rules! How embarrassing! Sorry, Physics Forums!
  4. Dec 25, 2011 #3
    Yep that's exactly what it is you can have to answers ±√.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook