document.write( "Question 664293: Given that the equation $\"kx%5E2%2B12x%2Bk=0\"$ where k is a positive constant and has equal roots. Find the value of k. \n" ); document.write( "

Algebra.Com's Answer #413236 by vleith(2983) $\"\"$ $\"About$

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You are told to find k such that the given equation results in two equal roots.
\n" ); document.write( "That says the resulting answer will end up being in the form $\"%28ax%2Bb%29%5E2+=+0\"$
\n" ); document.write( "So Let's expand that
\n" ); document.write( " $\"%28ax%2Bb%29%5E2+=+0\"$
\n" ); document.write( " $\"a%5E2x%5E2+%2B+2abx+%2B+b%5E2+=+0\"$
\n" ); document.write( "Now lets match that up with the given problem
\n" ); document.write( "We see that $\"k+=+a%5E2\"$ , $\"12+=+2ab\"$ , and $\"k+=+b%5E2\"$
\n" ); document.write( "We can see from this that $\"6=ab\"$ and also that $\"a%5E2+=+b%5E2\"$
\n" ); document.write( "Using the $\"a%5E2+=+b%5E2\"$ , we can see that either a=b or a=-b
\n" ); document.write( "Since a*b is positive (6), then a must be equal to b.\r
\n" ); document.write( "\n" ); document.write( "If a=b and ab =6, then a and b are both $\"sqrt%286%29\"$
\n" ); document.write( "So what does than make k? k is a^2 = 6.\r
\n" ); document.write( "\n" ); document.write( "Check our answer
\n" ); document.write( " $\"kx%5E2%2B12x%2Bk=0\"$
\n" ); document.write( " $\"6x%5E2+%2B+12x+%2B+6+=+0\"$
\n" ); document.write( " $\"x%5E2+%2B2x+%2B1+=+0\"$
\n" ); document.write( " $\"%28x%2B1%29%5E2+=+0\"$
\n" ); document.write( " \n" ); document.write( "

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