document.write( "Question 923905: G(x)=3x^2-4x-1 \n" ); document.write( "

Algebra.Com's Answer #560438 by Alan3354(69443) $\"\"$ $\"About$

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\n" ); document.write( "If you want to find the zeroes:
\n" ); document.write( "3x^2-4x-1 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"3x%5E2%2B-4x%2B-1+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-4%29%5E2-4%2A3%2A-1=28\"$ .
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\n" ); document.write( " Discriminant d=28 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28--4%2B-sqrt%28+28+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+28+%29%29%2F2%5C3+=+1.54858377035486\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%28-4%29-sqrt%28+28+%29%29%2F2%5C3+=+-0.21525043702153\"$
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\n" ); document.write( " Quadratic expression $\"3x%5E2%2B-4x%2B-1\"$ can be factored:
\n" ); document.write( " $\"3x%5E2%2B-4x%2B-1+=+%28x-1.54858377035486%29%2A%28x--0.21525043702153%29\"$
\n" ); document.write( " Again, the answer is: 1.54858377035486, -0.21525043702153.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-4%2Ax%2B-1+%29\"$

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