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Non-rational Quadratic (Posted on 2010-08-22) Difficulty: 2 of 5
Prove that the quadratic equation ax2 + bx + c = 0
does not have a rational root if a, b, and c are odd integers.

  Submitted by Bractals    
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Solution: (Hide)
Assume that p/q is a rational root of the equation with (p,q) = 1.
Then, ap2 + bpq + cq2 = 0. There are only three possible cases
for the integers p and q: both are odd or one is odd and the other
is even. In each of the three cases the sum of the three terms ap2,
bpq, and cq2 is odd. This contradicts the assumption that the sum
should be even. Therefore, the equation has no rational root.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtsre(2): Mod 4 .....back to 8Ady TZIDON2010-08-24 12:24:52
re: Mod 4Steve Herman2010-08-23 13:32:10
SolutionanswerDej Mar2010-08-23 04:09:24
SolutionMod 4Ady TZIDON2010-08-23 02:38:00
SolutionBy the numbers (spoiler)Steve Herman2010-08-22 21:21:50
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