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2022/23 AHSMC Part 1 Problem 4

Problem 4 of 16

For how many integers nn does the equation x2+nx+10=0 x^2 + nx + 10 = 0 have integer solutions?

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Solution

The product of the solutions must be 1010, which means that the solutions must be {±(1,10), ±(2,5)}. \{\pm(1,10),\ \pm(2,5)\}. This leads to n=±11n = \pm 11, ±7\pm 7. The answer is (E).

University of Alberta