# Maths - a proof question on the nature of roots of quadratic equations

1. Apr 14, 2012

### Eutrophicati

I'm sorry, I just realised I put this in the wrong subsection. While I figure out how to fix that, please have a look anyway.
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1. The problem statement, all variables and given/known data

Given x $\inℝ$
And s =$\frac{4(x^{2}) + 3}{2x-1}$
Prove that $s^{2}$ -4s - 12 ≥ 0

2. Relevant equations
The discriminant Δ, (in order for which to be real must be ≥ 0)
b^2 - 4ac ≥ 0

3. The attempt at a solution
Doing the algebra isn't the problem, I'm having trouble understanding the question itself. For this sort of proof, don't I need to work with
s =$\frac{4(x^{2}) + 3}{2x-1}$
instead of the statement to be proven, which is $s^{2}$ -4s - 12 ≥ 0?

In which case, how do I apply the b^2 - 4ac rule with the linear equation part in the denominator?

Last edited: Apr 14, 2012
2. Apr 15, 2012

The variable is $x$, so make the given equation look like a regular quadratic in $x$. Then pick off what $a$, $b$, and $c$ are and write the inequality for $\Delta$ in terms of those. It will quickly resolve into what's requested.