The equation x^2 + ax = −14 has only integer solutions for x. If a is a positive integer, what is the greatest possible value of a?
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The equation x^2 + ax = −14 has only integer solutions for x. If a is a positive integer, what is the greatest possible value of a?
x2 + ax = –14
x2 + ax + 14 = 0
The value of "a" is the sum of the integer factors of 14.
We want the positive factors so the sum will be positive.
That means either (1 + 14) or (2 + 7). 15 is the larger.
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