Question 114456
First step is to factor the trinomial.

{{{x^2 - 10x - 24 < 0}}}
{{{(x-12)(x+2)<0}}}


The trinomial, expressed as a function of x {{{f(x)=x^2 - 10x - 24}}} graphs as a parabola, convex up, that crosses the x-axis at (12,0) and (-1,0).  The zeros divide the x-axis into three intervals {{{-infinity<x<-1}}}, {{{-1<x<12}}}, {{{12<x<infinity}}}.


Since the inequality has the expression less than zero, we are interested in the interval where the graph is below the x-axis.  Since this is a concave up parabola (the a coefficient is positive), the desired interval is {{{-1<x<12}}}.  See graph.


{{{graph(400,400,-100,100,-100,100,x^2 - 10x - 24)}}}