X^3 -12X^2 + K

find K for

Two Different Zeros

Three Different Zeros ( I believe K=X for this one )

Only one Real Zero

Any help would be greatly appreciated thanks

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- Jul 17th 2012, 03:47 PMwaleedrabbaniFind K so that....
X^3 -12X^2 + K

find K for

Two Different Zeros

Three Different Zeros ( I believe K=X for this one )

Only one Real Zero

Any help would be greatly appreciated thanks - Jul 17th 2012, 04:27 PMWilmerRe: Find K so that....
- Jul 17th 2012, 04:31 PMReckonerRe: Find K so that....
The discriminant of the cubic equation $\displaystyle ax^3 + bx^2 + cx + d = 0$ is given by

$\displaystyle d = 18abcd - 4b^3d + b^2c^2 - 4ac^3 - 27a^2d^2.$

So the cubic equation $\displaystyle X^3 - 12X^2 + K$ has a discriminant of

$\displaystyle d = 6912K - 27K^2.$

Now determine which values of $\displaystyle K$ make the discriminant positive, negative, or zero.