Thread: Real 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?

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.

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.

0 < p < 32

bye