If f(x) = x^3 - 6x^2 + p , where P is an arbitrary constant. For what values of p does f(x) have 3 distinct real roots?

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- Apr 12th 2005, 09:30 PMneedhelpReal Roots
If f(x) = x^3 - 6x^2 + p , where P is an arbitrary constant. For what values of p does f(x) have 3 distinct real roots?

- Apr 14th 2005, 07:52 PMbeepnoodle
There is a general formula for the solution of a cubic, it is called Cardano's Formula. It would probably be a good place to start.

- Apr 15th 2005, 01:56 PMMathGuruGraphing
I would also suggest graphing this and getting an idea of how the curve can cross the x axis exactly three times. I'll try to attach a graph if I can.

- Apr 21st 2005, 12:43 PMtheprof
0 < p < 32

bye