document.write( "Question 888797: Find the value of a,b, or c so that each equation will have exactly one rational solution. p^2+bp+25=0\r
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Algebra.Com's Answer #537692 by richwmiller(17219) $\"\"$ $\"About$

You can put this solution on YOUR website!
p^2+10p+25=0
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ap%5E2%2Bbp%2Bc=0\"$ (in our case $\"1p%5E2%2B10p%2B25+=+0\"$ ) has the following solutons:
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\n" ); document.write( " $\"p%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
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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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%2810%29%5E2-4%2A1%2A25=0\"$ .
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\n" ); document.write( " Discriminant d=0 is zero! That means that there is only one solution: $\"p+=+%28-%2810%29%29%2F2%5C1\"$ .
\n" ); document.write( " Expression can be factored: $\"1p%5E2%2B10p%2B25+=+1%28p--5%29%2A%28p--5%29\"$
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\n" ); document.write( " Again, the answer is: -5, -5.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B10%2Ax%2B25+%29\"$

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