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
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.