SOLUTION: find nonzero integers A, B, C such that Ax^2+Bx+C=0 has solutions B and C

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Question 1139198: find nonzero integers A, B, C such that Ax^2+Bx+C=0 has solutions B and C
Answer by greenestamps(13200) (Show Source):
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In the quadratic equation

the sum of the roots is -B/A and the product of the roots is C/A.

If the roots are B and C, then

(1)
(2)

Equation (2) gives us

There are two possibilities with A and B both integers: they are both 1, or they are both -1.

If A = B = 1 then equation (1) gives us

Then the equation is

or

and the roots are B and C.

So there is one solution to the problem.

If A = B = -1, then equation (1) gives us

Since the requirement is that A, B, and C be non-zero, there is no solution in this case.

So the unique quadratic equation Ax^2+Bx+C=0 with roots B and C is .