if the equations x^2 - 4x + k =0 and 2x^2 - 3x + k =0 have a common root alpha,
find the value of k
F.4 a math 問題(1)
2007-05-22 2:27 am
回答 (2)
2007-05-22 2:54 am
✔ 最佳答案
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2007-05-22 2:47 am
By Sum of roots and product of roots rule,
The roots of x^2-4x+k = 0 is alpha and k/alpha.
The roots of 2x^2-3x+k = 0 is alpha and k/2alpha
Therefore,
alpha + k/alpha = 4 ---------- Equation1
alpha + k/2alpha = 3/2 ----- Equation2
Equation1-Equation2 = k/2alpha = 5/2
alpha = k/5 ----------------------- Equation3
Sub Equation3 into Equation1,
k/5 + 5 = 4
k = -5
The roots of x^2-4x+k = 0 is alpha and k/alpha.
The roots of 2x^2-3x+k = 0 is alpha and k/2alpha
Therefore,
alpha + k/alpha = 4 ---------- Equation1
alpha + k/2alpha = 3/2 ----- Equation2
Equation1-Equation2 = k/2alpha = 5/2
alpha = k/5 ----------------------- Equation3
Sub Equation3 into Equation1,
k/5 + 5 = 4
k = -5
參考: me
收錄日期: 2021-05-03 12:56:14
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