document.write( "Question 44814: How Do I tell what the answer and sign is to this.
\n" ); document.write( "(x-5)(x+2)<0. \n" ); document.write( "

Algebra.Com's Answer #29689 by adamchapman(301) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28x-5%29%28x%2B2%29%3C0\"$
\n" ); document.write( "Find the values where (x-5)(x+2)=0.
\n" ); document.write( "The answer is when x=-2 or x=5.
\n" ); document.write( "If you expand the brackets using FOIL; you get:
\n" ); document.write( " $\"x%5E2-3x-10%3C0\"$
\n" ); document.write( "in a qaudratic equation, if the amount of $\"x%5E2\"$ is positive (>0), the graph of that function has a 'smiley' shape. if the amount of x-squared's is negative (<0), the graph has a 'frown' shape:
\n" ); document.write( " $\"x%5E2%2Bx%2B1\"$ is happy:
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-2%2C+10%2C+x%5E2%2Bx%2B1%29+\"$
\n" ); document.write( " $\"-x%5E2%2Bx%2B1\"$ is frowning:
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+2%2C+-x%5E2%2Bx%2B1%29+\"$
\n" ); document.write( "If we condider the graph of our function $\"y=x%5E2-3x-10\"$ , we can see from the amount of $\"x%5E2\"$ 's that it is a 'happy' graph. The value of y is greater as we move out from the minimum point of the graph. We know that y=0 when x=-2 and x=5, and because of it's 'happy' shape, we can deduce that the function is <0 between these values of x.
\n" ); document.write( "So $\"x%5E2-3x-10%3C0\"$ when -2\n" ); document.write( "Check this with the graph of $\"y=x%5E2-3x-10\"$ :
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-4%2C+10%2C+-12%2C+5%2C+x%5E2-3x-10%29+\"$
\n" ); document.write( "I hope this helps.
\n" ); document.write( "P.S. In am currently constructing my own online tutoring website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
\n" ); document.write( "Adam
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