SOLUTION: Solve the inequality: x^2 - 10x - 24 < 0

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Question 114456: Solve the inequality: x^2 - 10x - 24 < 0
Found 2 solutions by edjones, solver91311:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)<0 when 2 < x < 12
See the graph.
Ed
graph%28500%2C500%2C-5%2C15%2C-50%2C10%2Cx%5E2-10x-24%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
First step is to factor the trinomial.
x%5E2+-+10x+-+24+%3C+0
%28x-12%29%28x%2B2%29%3C0

The trinomial, expressed as a function of x f%28x%29=x%5E2+-+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%3Cx%3C-1, -1%3Cx%3C12, 12%3Cx%3Cinfinity.

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%3Cx%3C12. See graph.

graph%28400%2C400%2C-100%2C100%2C-100%2C100%2Cx%5E2+-+10x+-+24%29