document.write( "Question 1085127: Find k such that the equation 6x^2 + 6x + k =0 has Two equal real roots, two distinct real roots, and no real roots. \n" ); document.write( "

Algebra.Com's Answer #699155 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"6x%5E2+%2B+6x+%2B+k+=0\"$ -> $\"a=6\"$ , $\"b=6\"$ , and $\"+c=k\"$ \r
\n" ); document.write( "\n" ); document.write( "if the discriminant $\"b%5E2-4ac%3E0\"$ , the equation has two distinct real roots\r
\n" ); document.write( "\n" ); document.write( " $\"6%5E2-4%2A6k%3E0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"36-24k%3E0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"36%3E24k\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k%3C36%2F24\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k%3C6%2F4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k%3C3%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k%3C1.5\"$ \r
\n" ); document.write( "\n" ); document.write( "so, we can try $\"k=1\"$ which is less than $\"k%3C1.5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"6x%5E2+%2B+6x+%2B+1+=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+6x%5E2+%2B+6x+%2B+1%29+\"$ \r
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\n" ); document.write( "\n" ); document.write( "if the discriminant $\"+b%5E2-4ac=0\"$ , the equation has two equal real roots\r
\n" ); document.write( "\n" ); document.write( " $\"6%5E2-4%2A6k=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"36-24k=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"36=24k\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k=36%2F24\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k=6%2F4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k=3%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k=1.5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+6x%5E2+%2B+6x+%2B+1.5%29+\"$ \r
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\n" ); document.write( "\n" ); document.write( "if the discriminant $\"b%5E2-4ac%3C0\"$ , there are no real solutions\r
\n" ); document.write( "\n" ); document.write( " $\"6%5E2-4%2A6k%3C0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"36-24k%3C0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"36%3C24k\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k%3E36%2F24\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k%3E6%2F4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k%3E3%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k%3E1.5\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"k=2\"$ ->\r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+6x%5E2+%2B+6x+%2B+2%29+\"$ \r
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