If α, β are the roots of x^2-4x+1=0, find quadratic equations in x with the following pairs of roots.
a) 2α+1, 2β+1
F.4 A MATHS
2006-10-17 3:38 am
回答 (2)
2006-10-17 3:43 am
✔ 最佳答案
α+β=4αβ=1
2α+1+2β+1
=2(α+β)+2
=10
(2α+1)(2β+1)
=4αβ+2(α+β)+1
=4+2(4)+1
=13
so quadratic equations in x with the following pairs of roots is
x^2-10x+13=0
2006-10-17 3:51 am
α+β= -4
αβ=1
2α+1+2β+1
=2(α+β+1)
=2(-3)
= -6
(2α+1)(2β+1)
=4αβ+2α+2β+1
=4+2(α+β)+1
=4-8+1
= -3
so quadratic equations in x with the following pairs of roots is
x^2-6x-3
2006-10-16 19:53:15 補充：
so quadratic equations in x with the following pairs of roots isx^2-6x-3=0
αβ=1
2α+1+2β+1
=2(α+β+1)
=2(-3)
= -6
(2α+1)(2β+1)
=4αβ+2α+2β+1
=4+2(α+β)+1
=4-8+1
= -3
so quadratic equations in x with the following pairs of roots is
x^2-6x-3
2006-10-16 19:53:15 補充：
so quadratic equations in x with the following pairs of roots isx^2-6x-3=0
參考: me
收錄日期: 2021-04-25 16:49:25
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