If one of the equation is the reciprocal of the other, find the possible values of k.
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F.4 Maths
2013-10-04 8:10 pm
Consider a quadratic equation 3x^2 -7x + k^2 - 2k = 0.
If one of the equation is the reciprocal of the other, find the possible values of k.
If one of the equation is the reciprocal of the other, find the possible values of k.
回答 (2)
2013-10-04 10:38 pm
✔ 最佳答案
Consider a quadratic equation3x^2－7x+k^2－2k= 0If one of the equation is the reciprocal of the other，findthe possible values of k.
Sol
設兩根p，1/p
p*1/p=(k^2－2k)/3=1
k^2－2k=3
k^2－2k－3=0
(k+1)(k－3)=0
k=－1 or k=3
2013-10-04 10:10 pm
let roots be s and 1/s
product of root = (s)(1/s) = k^2 - 2k = 1
solve k^2 - 2k = 1
k^2 - 2k + 1 = 1 + 1 add 1 to both side
(k-1)^2 = 2
k -1 = (+/-) root(2)
k = 1 (+/-) root(2)
2013-10-04 16:49:42 補充：
Sorry, 看漏了眼，product of root 應該為
product of root = (s)(1/s) = 1 = (k^2 - 2k)/3
k^2 - 2k = 3
k^2 - 2k -3 = 0
所以 螞蟻雄兵 才是正確的。
product of root = (s)(1/s) = k^2 - 2k = 1
solve k^2 - 2k = 1
k^2 - 2k + 1 = 1 + 1 add 1 to both side
(k-1)^2 = 2
k -1 = (+/-) root(2)
k = 1 (+/-) root(2)
2013-10-04 16:49:42 補充：
Sorry, 看漏了眼，product of root 應該為
product of root = (s)(1/s) = 1 = (k^2 - 2k)/3
k^2 - 2k = 3
k^2 - 2k -3 = 0
所以 螞蟻雄兵 才是正確的。
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