document.write( "Question 882989: When solving quadratic inequalities, how do I determine the direction of the symbol when writing the solutions out?
\n" ); document.write( "Ex: x^2+x -6<0
\n" ); document.write( "The solution is -3 (the opposite direction) Hope this makes sense\r
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Algebra.Com's Answer #533254 by josgarithmetic(39620) $\"\"$ $\"About$

You can put this solution on YOUR website!
You are looking for values of the quadratic function, LESS than zero. Think about this visually, like as a graph. The expression is a parabola opening upward, so the vertex is a minimum. The roots will be at y=0 and the vertex will be below the x-axis. \r
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\n" ); document.write( "\n" ); document.write( "You can factor the left side expression, so finding the roots is simple to do.
\n" ); document.write( " $\"x%5E2%2Bx-6=%28x-2%29%28x%2B3%29%3C0\"$
\n" ); document.write( "Which tells you that the roots or zeros are at x=2 and x=-3.
\n" ); document.write( "The solution is not -3 !\r
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\n" ); document.write( "\n" ); document.write( "You know you have a parabola opening upward with a minimum BETWEEN x=-3 and x=2.\r
\n" ); document.write( "\n" ); document.write( "LOOK at a graph of just the parabola function:
\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2%2Bx-6%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "The function or expression will be LESS THAN ZERO for x between -3 and positive 2.\r
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\n" ); document.write( "\n" ); document.write( "SOLUTION: $\"highlight%28highlight%28-3%3Cx%3C2%29%29\"$ .
\n" ); document.write( "You can also find the solution using the roots as critical points and testing any point in each interval which the critical points form. \n" ); document.write( "

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