F.4 Maths

Consider a quadratic equation3x^2－7x+k^2－2k= 0
If 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

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。