document.write( "Question 1134883: Show that the equation $\"+%289k-8%29x%5E2-6kx%2Bk%2B2=0+\"$ has roots which are different if $\"+k%3C8%2F5+\"$ \n" ); document.write( "

Algebra.Com's Answer #752389 by MathLover1(20849) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Show that the equation $\"+%289k-8%29x%5E2-6kx%2Bk%2B2=0+\"$ has roots which are different if $\"+k%3C8%2F5+\"$ \r
\n" ); document.write( "\n" ); document.write( "discriminant $\"b%5E2-4ac+\"$ shows you when equation has $\"2\"$ different roots \r
\n" ); document.write( "\n" ); document.write( "if you want distinct real roots, therefore the discriminant must be positive:\r
\n" ); document.write( "\n" ); document.write( " $\"b%5E2-4ac+%3E0\"$ \r
\n" ); document.write( "\n" ); document.write( "in your case $\"a=%289k-8%29\"$ , $\"b=6k\"$ , and $\"c=k%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( "so, $\"%286k%29%5E2-4%289k-8%29%28k%2B2%29+%3E0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"36k%5E2-%2836k-32%29%28k%2B2%29+%3E0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"36k%5E2-%2836+k%5E2+%2B+40+k+-+64%29+%3E0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"36k%5E2-36k%5E2+-40k+%2B64+%3E0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+-40k+%2B64+%3E0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+64+%3E40k\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k%3C64%2F40\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k%3C8%2F5\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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