Coefficient Cubic Roots

Algebra Level 5

How many triples of real numbers (a,b,c)(a,b,c) are there such that a,b, and ca,b, \mbox{ and}\ c are the roots of the equation x3+ax2+bx+c=0x^3 + ax^2 + bx + c = 0?

Details and assumptions

The roots are counted with multiplicity.

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