document.write( "Question 1090260: factor 2x^(2)-3x+3=0 \n" ); document.write( "
Algebra.Com's Answer #704704 by greenestamps(13200)\"\" \"About 
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Every quadratic equation has two solutions; every quadratic expression can be factored. But nearly always when we are asked to factor a quadratic, we want to factor it \"over the integers\". And while every quadratic expression can be factored, very few can be factored over the integers.
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\n" ); document.write( "So I think the answer to your question is that your quadratic expression can't be factored.
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\n" ); document.write( "I assume you are familiar with the quadratic formula, and with the discriminant, b^2-4ac. A quadratic expression can be factored over the integers if and only if the discriminant is a perfect square (so that the square root of the discriminant is an integer).
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\n" ); document.write( "In your quadratic, b^2-4ac is -15. So not only can the expression not be factored over the integers; but also the negative value of the discriminant means the zeros of the expression (the roots of the equation) are complex.
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\n" ); document.write( "The quadratic formula gives the two roots of your example as
\n" ); document.write( "\"x=%283%2B-i%2Asqrt%2815%29%29%2F4\"
\n" ); document.write( "or
\n" ); document.write( "\"x=3%2F4%2B-i%2Asqrt%2815%29%2F4\"
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\n" ); document.write( "Then, if you wanted a factored form of your quadratic equation, even though the roots are complex, it would be
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\n" ); document.write( "\"2%28x-%283%2Bi%2Asqrt%2815%29%29%2F4%29%28x-%283-i%2Asqrt%2815%29%29%2F4%29=0\" \n" ); document.write( "

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