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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?
Wiki User
∙ 6y ago
I think you mean the roots are prime numbers.
Let the two roots be primes p and q
Then the equation factorises to (x - p)(x - q) = 0 which can be expanded to give:
x² - (p + q)x + pq = 0
Which comparing coefficients of the original gives:
a = p + q
2b = pq
as 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 2 as 2 is the ONLY even prime
Assume p is an even prime, ie p = 2
→ a = 2 + q
2b = 2q → b = q
→ a - b = (2 + q) - q = 2
(It doesn't matter if the other prime is even (2) or not as it cancels out from a - b.)
Wiki User
∙ 6y ago
Wiki User
∙ 6y agoIt is 2.
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