document.write( "Question 42856: Solve 3x^2-8x+4=0 by graphing. If the exact roots cannot be found, state the consecutive integers between which the roots are located.\r
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Algebra.Com's Answer #27937 by atif.muhammad(135) $\"\"$ $\"About$

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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"3x%5E2%2B-8x%2B4+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-8%29%5E2-4%2A3%2A4=16\"$ .
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\n" ); document.write( " Discriminant d=16 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28--8%2B-sqrt%28+16+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+16+%29%29%2F2%5C3+=+2\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%28-8%29-sqrt%28+16+%29%29%2F2%5C3+=+0.666666666666667\"$
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\n" ); document.write( " Quadratic expression $\"3x%5E2%2B-8x%2B4\"$ can be factored:
\n" ); document.write( " $\"3x%5E2%2B-8x%2B4+=+3%28x-2%29%2A%28x-0.666666666666667%29\"$
\n" ); document.write( " Again, the answer is: 2, 0.666666666666667.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-8%2Ax%2B4+%29\"$

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\n" ); document.write( "\n" ); document.write( "Therefore, the roots are 2 and 0.7 (between 0 and 1). \n" ); document.write( "

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