Factorial of Quadratic Expression
Find the sum of all values of for the equation:
Clarification : The factorial in this problem is defined for integers (i.e. the Gamma function is not considered).
The answer is -10.
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Solving y ! = 1
The solutions y = 1 and y = 0 are appearent by inspection. It is easily seen that there are no other positive solutions, as the factotrial increases uniformly over the positive integers.
Using only the integral solutions, we have x 2 + 5 x + 6 = 1 and x 2 + 5 x + 6 = 0 . By Vietas, the sum of the roots of both of these equations is − 1 0 .