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Given that the quadratic equation x^2 + kx - (k - 3) = 0 has real roots α and β. If lαl = lβl, find the values of k.
A MATH
2007-09-27 4:47 am
回答 (1)
2007-09-27 4:59 am
✔ 最佳答案
Case 1: α = βSum of roots = 2α = -k, i.e. α = -k/2
Product of roots = 3-k = α^2
3-k = k^2/4
k^2 = 12-4k
k^2 - 4k - 12 = 0
k = 6 or -2
Case 2: α = -β, i.e. α + β = 0
Hence Sum of roots = -k = 0
k = 0
When k = 0, the equation becomes x^2 + 3 = 0, which has no real roots.
Hence "k = 0" is rejected
Therefore, k = 6 or -2
參考: me
收錄日期: 2021-04-13 18:12:00
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https://hk.answers.yahoo.com/question/index?qid=20070926000051KK05131