Numerical answer
The two roots of the quadratic equation x² − 11x + b = 0 are positive integers that differ by 3. Find the value of b.
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Answer: 28
Let the roots be p and q with p + q = 11 (sum of roots = −(−11)/1 = 11) and p − q = 3. Solving, p = 7, q = 4. Product of roots = b/1 = pq = 7 × 4 = 28. Check: x² − 11x + 28 = (x−7)(x−4) = 0, roots 7 and 4, which indeed differ by 3. So b = 28.
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