document.write( "Question 257636: For what values of k are the roots of 2x^2-3x + k = 0 equal? \n" ); document.write( "

Algebra.Com's Answer #189528 by richwmiller(17219) $\"\"$ $\"About$

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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"2x%5E2%2B3x%2B1.125+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%283%29%5E2-4%2A2%2A1.125=0\"$ .
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\n" ); document.write( " Discriminant d=0 is zero! That means that there is only one solution: $\"x+=+%28-%283%29%29%2F2%5C2\"$ .
\n" ); document.write( " Expression can be factored: $\"2x%5E2%2B3x%2B1.125+=+2%28x--0.75%29%2A%28x--0.75%29\"$
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\n" ); document.write( " Again, the answer is: -0.75, -0.75.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B1.125+%29\"$

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