Really how?
How many polynomials in the form , where and are integers are there such that three of the roots are distinct positive integers?
The answer is 4.
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1 solution
The roots of the equation add up to 10 and are all distinct positive integers.
The question, then just reduces to finding the number of sets of distinct integers which satisfy this condition.
Clearly, ( 1 , 2 , 7 ) ( 1 , 3 , 6 ) ( 1 , 4 , 5 ) ( 2 , 3 , 5 ) are the required sets. Hence, 4 is our answer.