If the equation x2 minus ax plus 2b equals 0 has prime roots where a and b are positive integers then a minus b is equal to?

If the equation x2 minus ax plus 2b equals 0 has prime roots where a and b are positive integers then a minus b is equal to?
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I think you mean the roots are prime numbers.Let the two roots be primes p and qThen the equation factorises to (x - p)(x - q) = 0 which can beexpanded to give:x² - (p + q)x + pq = 0Which comparing coefficients of the original gives:a = p + q2b = pqas b is an integer, pq must be even,→ at least one of p or q must be even→ as they are both primes and at least one is even, it MUST be 2as 2 is the ONLY even primeAssume p is an even prime, ie p = 2→ a = 2 + q2b = 2q → b = q→ a - b = (2 + q) - q = 2(It doesn't matter if the other prime is even (2) or not as itcancels out from a - b.)
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