更新1:
If f(1-√2)=0 and f(-1-√2)=0, find a polynomial f(x) with the least degree and integral coefficients?
lf f(1-√2)=0 and f(-1-√2)=0, find f(x) with the least degree and integral coefficients?
回答 (3)
2015-04-06 5:37 pm
1 + 2 Sqrt[2] x + x^2
2015-04-06 5:35 pm
if you have integer coefficients then these these the conjugates must also be roots.
ie f(1 + sqrt 2) = 0 and (-1 + sqrt 2) = 0
(x - 1 + sqrt 2)(x -1 - sqrt 2)(x + 1 + sqrt 2)(x +1 - sqrt 2)
(x^2 - 2x - 1)(x^2 + 2x -1)
f(x) = x^4 - 6x^2 +4x +1
ie f(1 + sqrt 2) = 0 and (-1 + sqrt 2) = 0
(x - 1 + sqrt 2)(x -1 - sqrt 2)(x + 1 + sqrt 2)(x +1 - sqrt 2)
(x^2 - 2x - 1)(x^2 + 2x -1)
f(x) = x^4 - 6x^2 +4x +1
2015-04-06 5:28 pm
2
收錄日期: 2021-04-29 00:00:49
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150406092315AAKEUXL