It is given that 1/α and 1/β are the roots of the quadratic equation x²－x－3＝0.
（b）Form a quadratic equation In x whose roots are α and β.
請求各位大大教我做這條數學題目，謝謝解答。?
2016-10-16 11:56 am
回答 (1)
2016-10-16 1:56 pm
✔ 最佳答案
Soly=1/x
x=1/y
x^2－x－3=0
(1/y)^2－(1/y)－3=0
1/y^2－1/y－3=0
1－y－3y^2=0
3y^2+y－1=0
3x^2+x－1=0
or
1/(αβ)=－3
αβ=－1/3
1/α+1/β=1
(α+β)/(αβ)=1=－3(α+β)
α+β=－1/3
x^2－(α+β)x+αβ=0
x^2+x/3－1/3=0
3x^2+x－1=0
收錄日期: 2021-04-20 16:34:27
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20161016035646AAQgnwa