Beginner mathematics.
If and are primes and has distinct positive integral roots, find .
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1 solution
If we factor out the equation, we will get ( x − q ) ( x − 1 ) , because q is a prime, and its only factors are itself and one. Now, if we multiply ( x − q ) ( x − 1 ) out, we will get x 2 − ( q + 1 ) x + q , so p = q + 1 , and the only primes 1 apart from each other are 2 and 3 . Therefore, p = 2 , and q = 3 .