F4數學.Quadratic equation.

👨🏻‍🏫 學術台數學

[匿名]

2009-11-02 12:38 am

The sum of roots of the equation 2x^2-4x+k=0 is twice the difference of the roots.Find the value of k and the roots.

更新1:

sorry.我唔明呢度... (a - b)2 = 1 (a + b)2 - 4ab = 1 4 - 2k = 1 k = 3/2

更新2:

明了.thz!

回答 (2)

六呎將軍

2009-11-02 12:59 am

✔ 最佳答案

Let the roots be a and b, then:

a + b = 2(a - b)

2(a - b) = 2

a - b = 1

(a - b)2 = 1

(a + b)2 - 4ab = 1

4 - 2k = 1

k = 3/2

2009-11-01 17:14:11 補充：
The equation is now:
2x^2-4x+3/2=0
4x^2-8x+3=0
(2x-3)(2x-1)=0
x = 3/2 or 1/2

參考: Myself

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用戶2053

2009-11-02 1:11 am

and the roots ???

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收錄日期: 2021-04-21 22:07:11
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