Rational roots - standard form of equation

[Janinever]

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!

 

[pwsnafu]

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

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

 

[Janinever]

Thank you!