Thread: inequality

1. inequality

Hello!
Please help me to solve this inequality!
p(x^2+2)<2x^2+6x+1, if p is parameter!

2. You want to solve for $x$?

3. yes!

4. Do you know the quadratic formula?

When you have $ax^2+bx+c=0,x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In your case.

$p(x^2+2)<2x^2+6x+1$

$px^2+2p<2x^2+6x+1$

$0<2x^2-px^2+6x+1-2p$

$2x^2-px^2+6x+1-2p<0$

$(2-p)x^2+6x+1-2p<0$

Now use $a = 2-p, b=6, c = 1-2p$ into the quadratic formula