document.write( "Question 144718: Determine whether the following equations have a solution or not? Justify your answer.
\n" ); document.write( " 5x2 + 8x + 7 = 0 \r
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Algebra.Com's Answer #105454 by solver91311(24713) $\"\"$ $\"About$

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Of course there is a solution, in fact there are two solutions -- there always are when you have a quadratic equation. The fundamental theorem of algebra tells us that for a polynomial equation of degree $\"n\"$ there are always $\"n\"$ solutions.\r
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\n" ); document.write( "\n" ); document.write( "In this case, however, there are no REAL number solutions. That is because the discriminant, i.e. the expression under the radical in $\"x+=+%28-b+%2B-+sqrt%28red%28+b%5E2-4ac%29+%29%29%2F%282a%29+\"$ , is less than zero:\r
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\n" ); document.write( "\n" ); document.write( " $\"red%28b%5E2-4ac%29=64-140=-76%3C0\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Hence, the two roots of the given equation are a conjugate pair of complex numbers of the form $\"alpha%2B-beta%28i%29\"$ , where $\"alpha\"$ and $\"beta\"$ are real number coefficients and $\"i\"$ is the imaginary number defined by $\"i%5E2=-1\"$ \n" ); document.write( "

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