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Equation 2 p in a q?

Updated: 9/18/2023
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13y ago

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2 Pints in a Quart

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Q: Equation 2 p in a q?
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Solve for p and q. 2p plus 3q equals 13 and 5p - 4q equals -2?

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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?

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.)