document.write( "Question 763896: find the value of k for which the roots are real and equal in the equation 12x^2+4kx+3=0 \n" ); document.write( "

Algebra.Com's Answer #465099 by fcabanski(1391) $\"\"$ $\"About$

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For the roots of a quadratic equatioin (ax^2 +bx + c) to be equal and real, the discriminant of the equation must be 0. The discriminant is the part under the square root sign in the quadratic formula:

\n" ); document.write( "b^2 - 4ac

\n" ); document.write( "For this equation b= 4k, a=12 and c=3

\n" ); document.write( " $\"%284k%29%5E2+-+4%2A12%2A3+=+0\"$

\n" ); document.write( " $\"16k%5E2+-+144+=+0\"$

\n" ); document.write( " $\"16k%5E2+=+144\"$

\n" ); document.write( " $\"k%5E2+=+9\"$

\n" ); document.write( "k = 3 or -3

\n" ); document.write( "A k value of 3 or -3 results in two real roots that are equal. \n" ); document.write( "

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