document.write( "Question 246910: Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.\r
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Algebra.Com's Answer #180221 by richwmiller(17219) $\"\"$ $\"About$

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t2 + 4t + 4 = 0
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"1x%5E2%2B4x%2B4+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%284%29%5E2-4%2A1%2A4=0\"$ .
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\n" ); document.write( " Discriminant d=0 is zero! That means that there is only one solution: $\"x+=+%28-%284%29%29%2F2%5C1\"$ .
\n" ); document.write( " Expression can be factored: $\"1x%5E2%2B4x%2B4+=+1%28x--2%29%2A%28x--2%29\"$
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\n" ); document.write( " Again, the answer is: -2, -2.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B4+%29\"$

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