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This is a math problem I received during a math team meet as practice. I spent an hour on it with no luck. Does anyone have any ideas?
The polynomial function f(x) = x^3 + ax^2 + bx + c has the following properties:
1. At least two of its zeros are distinctive
2. The sum of its zeros is twice the product of its zeros
3. The sum of the squares of the zeros is three times the product of its zeros
4. f(1) = 1
Find the numerical value of c