Rational roots - standard form of equation

  1. Hi everybody!

    I've hit a blank with regards to this 1 equation on a old exam paper - think I've overloaded myself a bit and just feel a bit like a airhead at the moment!

    I understand the actual method and getting to the answer but it starts off with a equation which you then need to get to a standard form to use the formula to check if the roots are rational.

    The initial equation is this :

    4x^2 + 2kx - k = 2x

    Then on the memorandum this is taken to standard form so the info can be substituted into the formula Δ = b^2 - 4ac

    the standard form they then write that initial equation in is :

    4x^2 + 2(k-1)x-k = 0

    How do they get from 4x^2 + 2kx - k = 2x to this 4x^2 + 2(k-1)x-k = 0

    The rest I understand entirely. Literally just the above has be scratching my head!

    Please help :)

    Thank you!
     
  2. jcsd
  3. pwsnafu

    pwsnafu 933
    Science Advisor

    Sometimes you overlook the obvious answers. Just subtract 2x from both sides.
     
  4. Thank you!
     
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