document.write( "Question 72473: x2-2x+3=0 \n" ); document.write( "

Algebra.Com's Answer #51808 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Use the quadratic formula to find the roots (polynomial cannot be factored)
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"1x%5E2%2B-2x%2B3+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-2%29%5E2-4%2A1%2A3=-8\"$ .
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\n" ); document.write( " The discriminant -8 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 -8 is + or - $\"sqrt%28+8%29+=+2.82842712474619\"$ .
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\n" ); document.write( " The solution is

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\n" ); document.write( " Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B3+%29\"$

\n" ); document.write( "\n" ); document.write( "In other words, this polynomial has no real roots (real numbers as roots), it only has complex roots. \n" ); document.write( "

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