document.write( "Question 570721: For what values of K does the equation have equal solutions? 2x^2-Kx+8=0 \n" ); document.write( "

Algebra.Com's Answer #367743 by josmiceli(19441) $\"\"$ $\"About$

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When the equation has the form $\"+f%28x%29+=+ax%5E2+%2B+bx+%2B+c+\"$ ,
\n" ); document.write( "The quadratic formula to find the roots is
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "For real solutions, $\"+b%5E2+-+4a%2Ac+\"$ must be $\"+0+\"$ or positive
\n" ); document.write( "given:
\n" ); document.write( " $\"+2x%5E2+-+K%2Ax+%2B+8+=+0+\"$
\n" ); document.write( " $\"+b%5E2+-+4a%2Ac+=+%28-K%29%5E2+-+4%2A2%2A8+\"$
\n" ); document.write( " $\"+b%5E2+-+4a%2Ac+=+K%5E2+-+64+\"$
\n" ); document.write( "To be positive or zero,
\n" ); document.write( " $\"+K%5E2+-+64+%3E=+0+\"$
\n" ); document.write( " $\"+K%5E2+%3E=+64+\"$
\n" ); document.write( " $\"+K+%3E=+8+\"$
\n" ); document.write( "and, also, using (-) root
\n" ); document.write( " $\"+K+%3C=+-8+\"$
\n" ); document.write( "so,
\n" ); document.write( " $\"+8+%3C=+K+%3C=+-8+\"$ \n" ); document.write( "

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