document.write( "Question 369077: the roots 2x^2-3x+c=0 are imaginary if c equals \n" ); document.write( "

Algebra.Com's Answer #263012 by jsmallt9(3758) $\"\"$ $\"About$

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$\"b%5E2-4ac\"$ is called the discriminant. Its value will tell you how many roots of what type there are for a quadratic equation:

$\"b%5E2-4ac+%3E+0\"$ means that there are two real roots.
$\"b%5E2-4ac+=+0\"$ means that there are one real root.
$\"b%5E2-4ac+%3C+0\"$ means that there are two complex roots. And if b = 0 then the complex roots are imaginary roots (i.e. the real part of the complex number will be zero).

\n" ); document.write( "The a, b and c for the discriminant come from the general form for quadratic equations: $\"ax%5E2+%2B+bx+%2B+c+=+0\"$ . Looking at your equation, a = 2, b = -3 and c = c. This makes the discriminant:
\n" ); document.write( " $\"%28-3%29%5E2+-4%282%29%28c%29\"$
\n" ); document.write( "which simplifies as follows:
\n" ); document.write( " $\"9+-+4%282%29c\"$
\n" ); document.write( " $\"9+-+8c\"$
\n" ); document.write( "If we want complex roots then we want
\n" ); document.write( " $\"9+-+8c+%3C+0\"$
\n" ); document.write( "Solving this I'll start by subtracting 9 from each side:
\n" ); document.write( " $\"-8c+%3C+-9\"$
\n" ); document.write( "Then dividing by -8. (Remember that whenever an inequaity is multiplied or divided by any negative number, like we are doing now, the inequality symbol must be reversed! This is why we have a \"greater than\" all of a sudden.)
\n" ); document.write( " $\"c+%3E+9%2F8\"$

\n" ); document.write( "NOTE: Since your b is not zero, there is no way to get imaginary roots. \n" ); document.write( "

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