Question 113449

{{{x ^2 -3x-4 < 0}}}

We need to solve it as an equation and find roots.

{{{x ^2 -3x-4 = 0}}}


Here is the solution with graph:


*[invoke quadratic_formula 1, -3, -4, "x"]


As you can see, your solutions are: {{{x[1] = 4}}} and {{{x[2] = -1}}}

For these values {{{x ^2 -3x-4}}} will be equal to {{{ 0}}}. That means for all values of {{{x}}} from {{{-1}}} (excluding {{{-1}}}) to {{{4}}} (excluding {{{4}}}), you will have {{{x ^2 -3x-4}}} less than {{{0}}}.

or {{{x ^2 -3x-4 < 0}}} for {{{-1< x < 4}}}

As you can see on graph, that part of the parabola lies in III-th and IV-th quadrant (under x-axis)