Abstract
In this work, we employ a well known result due to Zagier to derive an asymptotic formula for the average number of divisors of a quadratic polynomial of the form $$x^{2}-bx+c$$ with $$b,\,c$$ integers. As simple consequences, we obtain formulas for computing the narrow class number of a quadratic field and relations between the narrow class number and a weighted class number for binary quadratic forms considered by McKee. In the end, we employ the class number relation to compute several examples of the weighted class number.
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