How many ordered triplets $(a,b,c)$ of rational numbers are there where $a,b,c$ are the roots of $x^3 + ax^2 + bx + c = 0?$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
How many ordered triplets $(a,b,c)$ of rational numbers are there where $a,b,c$ are the roots of $x^3 + ax^2 + bx + c = 0?$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3
How many ordered triplets $(a,b,c)$ of rational numbers are there where $a,b,c$ are the roots of $x^3 + ax^2 + bx + c = 0?$
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