Let
be a polynomial with odd integral coefficients,show that it cannot have rational root.
訂閱：
張貼留言 (Atom)
數學資料庫 (http://www.mathdb.org/ 及 http://eng.mathdb.org/)是香港其中一個最大型的數學網站，由一班來自香港各間大學及美國多間大學的數學系、物理系、精算系、建築系、電子工程系的學生建立。數學資料庫旨在於網上提供豐富的數學資源。我們上載了不同種類和數學相關的教學資料，是同學們一個好的參考網站。
5 則留言:
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 =b
b is odd but AD+BC is even.
Therefore, contradiction.
張貼留言