document.write( "Question 194126: What type of solutions do you get from a quadratic equation where D < 0? Give reasons for your answer. Also provide an example of such a quadratic equation and find the solutions of the equation. Thank You \n" ); document.write( "
Algebra.Com's Answer #145704 by Mathtut(3670)\"\" \"About 
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when the discriminant is less than zero you get two complex solutions
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\n" ); document.write( "\"x%5E2%2B3x%2B7=0\" would be one such example
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\n" ); document.write( "\"3%5E2-4%281%29%287%29=-19\"
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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 \"1x%5E2%2B3x%2B7+=+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%2A1%2A7=-19\".
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\n" ); document.write( " The discriminant -19 is less than zero. That means that there are no solutions among real numbers.

\n" ); document.write( " If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

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\n" ); document.write( " In the field of imaginary numbers, the square root of -19 is + or - \"sqrt%28+19%29+=+4.35889894354067\".
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\n" ); document.write( " The solution is , or
\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%2B3%2Ax%2B7+%29\"
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