document.write( "Question 549684: What should be the range of the value of k so that the equation 2x2+3kx-9=0 will have real and unequal roots?
\n" ); document.write( "What should be the value of k so that the equation x2+(k-2)x+4=0 will have equal roots?
\n" ); document.write( "Find the range of the value of k so that the equation kx2+4squareroot of 3x+k=0 will have imaginary roots.
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Algebra.Com's Answer #357971 by KMST(5328) $\"\"$ $\"About$

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The discriminant for $\"2x%5E2%2B3kx-9=0\"$ is
\n" ); document.write( " $\"%283k%29%5E2-4%2A2%2A%28-9%29=9k%5E2%2B72\"$
\n" ); document.write( "The equation $\"2x%5E2%2B3kx-9=0\"$ will have real and unequal roots when
\n" ); document.write( " $\"9k%5E2%2B72%3E0\"$ which happens for all real values of k.
\n" ); document.write( "The discriminant for $\"x%5E2%2B%28k-2%29x%2B4=0\"$ is
\n" ); document.write( " $\"%28k-2%29%5E2-4%2A1%2A4=%28k-2%29%5E2-16\"$
\n" ); document.write( "The equation $\"x%5E2%2B%28k-2%29x%2B4=0\"$ will have equal roots when
\n" ); document.write( " $\"%28k-2%29%5E2-16=0\"$ <--> $\"%28k-2%29%5E2=16\"$ which happens for $\"k=6\"$ and $\"k=-2\"$
\n" ); document.write( "Was the third equation $\"kx%5E2%2B4sqrt%283%29x%2Bk=0\"$ ?
\n" ); document.write( "The discriminant for $\"kx%5E2%2B4sqrt%283%29x%2Bk=0\"$ is
\n" ); document.write( " $\"%284sqrt%283%29%29%5E2-4%2Ak%2Ak=48-4k%5E2=4%2812-k%5E2%29\"$
\n" ); document.write( "The equation $\"kx%5E2%2B4sqrt%283%29x%2Bk=0\"$ will have imaginary roots when
\n" ); document.write( " $\"12-k%5E2%3C0\"$ , which happens for $\"abs%28k%29%3Esqrt%2812%29=2sqrt%283%29\"$ \n" ); document.write( "

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