document.write( "Question 471511: Find all intercepts for the graph of the quadratic function.
\n" ); document.write( "f(x) = 5x2 – 38x + 21 \n" ); document.write( "

Algebra.Com's Answer #323382 by jorel1380(3719) $\"\"$ $\"About$

You can put this solution on YOUR website!
5x2-38x+21=0
\n" ); document.write( "(5x-3)(x-7)=0
\n" ); document.write( "x=3/5 or 7
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"5x%5E2%2B-38x%2B21+=+0\"$ ) has the following solutons:
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\n" ); document.write( " $\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
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\n" ); document.write( " For these solutions to exist, the discriminant $\"b%5E2-4ac\"$ should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-38%29%5E2-4%2A5%2A21=1024\"$ .
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\n" ); document.write( " Discriminant d=1024 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28--38%2B-sqrt%28+1024+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%28-38%29%2Bsqrt%28+1024+%29%29%2F2%5C5+=+7\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%28-38%29-sqrt%28+1024+%29%29%2F2%5C5+=+0.6\"$
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\n" ); document.write( " Quadratic expression $\"5x%5E2%2B-38x%2B21\"$ can be factored:
\n" ); document.write( " $\"5x%5E2%2B-38x%2B21+=+5%28x-7%29%2A%28x-0.6%29\"$
\n" ); document.write( " Again, the answer is: 7, 0.6.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-38%2Ax%2B21+%29\"$

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