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related to Newton polytope?
You may use similar method of proving root 2 is not a rational number to solve this problem.
the aim is to prove the sq root of delta is irrational ?actually i can not solve this problem by the method contradiction...
Suppose there is a rational root x=p/q, where p, q are relatively prime integer. put x=p/q into the polynomial.Note: a, b and c are odd integral coeff.finally check the parity.
Suppose LHS can be factorized into (Ax+B)(Cx+D), where A, B, C & D are integers.Then since a & c are odd, all A, B, C & D must be odd.Expand to get the coeff. of x = AD+BC =bb is odd but AD+BC is even.Therefore, contradiction.
related to Newton polytope?
回覆刪除You may use similar method of proving root 2 is not a rational number to solve this problem.
回覆刪除the aim is to prove the sq root of delta is irrational ?
回覆刪除actually i can not solve this problem by the method contradiction...
Suppose there is a rational root x=p/q, where p, q are relatively prime integer.
回覆刪除put x=p/q into the polynomial.
Note: a, b and c are odd integral coeff.
finally check the parity.
Suppose LHS can be factorized into (Ax+B)(Cx+D), where A, B, C & D are integers.
回覆刪除Then since a & c are odd, all A, B, C & D must be odd.
Expand to get the coeff. of x = AD+BC =b
b is odd but AD+BC is even.
Therefore, contradiction.