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Discriminants (Posted on 2005-05-24) Difficulty: 2 of 5
Consider a quadratic equation with integer coefficients.
Is every integer a possible discriminant?

Prove it.

See The Solution Submitted by Jer    
Rating: 3.3333 (3 votes)

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Solution Four | Comment 3 of 7 |
For b^2-4ac to be an even integer, b^2 must be even. Thus b must be even. Therefore, b^2-4ac = (2k)^2-4ac = 4(k^2-ac) for some integer k. Hence, any even integer not divisible by 4 cannot be a discriminant.
  Posted by Bractals on 2005-05-25 05:24:26
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