Write your own Python program where a non-intrinsic function solves for all the roots of a cubic polynomial given by the mathematical function g(x)=ax³+bx²+cx+d where a,b,c and d are nonzero real numbers given by the user. Afterwards, the program will also solve for the sum and product of these roots. You must be able to create a function for getting the sum, and another for the product and use it in your main program. (HINT: Use Cardano's formula).

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