Find the value of k, for which one root of the quadratic equation kx2-14x+8=0 is six times the other.?
回答 (1)
2016-02-26 3:27 pm
Let α and 6α be the two roots of the equation.
Sum of the roots :
α + 6α = 14/k
7α = 14/k
α = 2/k
α² = 4/k² ...... [1]
Product of the roots :
α * (6α) = 8/k
α² = 4/3k ...... [2]
[1] = [2] :
4/k² = 4/3k
k² = 3k
k² - 3k = 0
(k - 3)k = 0
k = 3 or k = 0 (rejected, for it is not a quadratic equation when k = 0)
Thus, k = 3
Sum of the roots :
α + 6α = 14/k
7α = 14/k
α = 2/k
α² = 4/k² ...... [1]
Product of the roots :
α * (6α) = 8/k
α² = 4/3k ...... [2]
[1] = [2] :
4/k² = 4/3k
k² = 3k
k² - 3k = 0
(k - 3)k = 0
k = 3 or k = 0 (rejected, for it is not a quadratic equation when k = 0)
Thus, k = 3
收錄日期: 2021-04-18 14:30:09
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160226071744AA3K790