Question

Find p such that one root of x^2-(p+1)x+p^2+p-8=0 is greater than 2 and other root is smaller than 2

Answer 1

If you make a graph, the parabola must be below the x-axis for $x=2$, so your statement means that $f(2) < 0$. This is the first condition.

The second condition is that the equation must have two roots, so the discriminant is positive. $D>0$

Use these two conditions to find the appropriate values of $p$.