document.write( "Question 978529: \"The equation x^2-3x+k^2=4 has two distinct real roots. Find the possible values of k.\" I've already tried plugging in small integers such as ą1 and ą2 which has yielded answers but I want to know how to properly approach the problem and obtain all the possible solutions. Thanks. \n" ); document.write( "

Algebra.Com's Answer #599898 by josgarithmetic(39617) $\"\"$ $\"About$

You can put this solution on YOUR website!
Completely general-form quadratic equation:
\n" ); document.write( " $\"x%5E2-3x%2Bk%5E2-4=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "Use the discriminant for finding the answer to the question. You want a discriminant that is POSITIVE.\r
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\n" ); document.write( "\n" ); document.write( "Discriminant, $\"%28-3%29%5E2-4%2A1%2A%28k%5E2-4%29%3E0\"$ .
\n" ); document.write( "Simplify, $\"9-4%28k%5E2-4%29%3E0\"$
\n" ); document.write( " $\"9-4k%5E2%2B16%3E0\"$
\n" ); document.write( " $\"-9%2B4k%5E2-16%3C0\"$
\n" ); document.write( " $\"4k%5E2%3C25\"$
\n" ); document.write( " $\"k%5E2%3C25%2F4\"$ ----Last good step before mistake.
\n" ); document.write( " $\"cross%28k%3C5%2F4%29\"$ , $\"k%3C5%2F2\"$ , bu a more complete and correct solution here is $\"cross%28-5%2F4%3Ck%3C5%2F4%29\"$ $\"highlight%28-5%2F2%3Ck%3C5%2F2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Your trial of k=-1 or k=1 will work.
\n" ); document.write( "Your trial of k=-2 or k=2 will also work.\r
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\n" ); document.write( "\n" ); document.write( "--
\n" ); document.write( "simply staying with $\"k%3C5%2F2\"$ is not adequate. It would include too many incorrect values. \n" ); document.write( "

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