標題:
F4 A.maths (Quadratic equation)
發問:
Given that one root of the equation x^2 + kx - 6 = 0 is the reciprocal of a root of the equation 2x^2 + kx - 1 = 0. Find the values of k.
最佳解答:
此文章來自奇摩知識+如有不便請留言告知
Let the root in x2 + kx - 6 = 0 be a and in that of 2x2 + kx - 1 = 0 be 1 / a. So, a2 + ak – 6 = 0 ak = 6 – a2 k = ( 6 – a2 ) / a --- ( 1 ) 2 ( 1 / a )2 + k ( 1 / a ) – 1 = 0 2 / a2 + k / a – 1 = 0 2 + ka – a2 = 0 ka = a2- 2 k = ( a2 - 2 ) / a --- ( 2 ) Put ( 1 ) into ( 2 ), ( 6 – a2 ) / a = ( a2 – 2 ) / a 6 – a2 = a2 – 2 2a2 = 8 a2 = 4 a = 2 or –2 k = ( 22 – 2 ) / 2 = 1 or [ ( - 2 )2 – 2 ] / ( - 2 ) = -1
其他解答:
文章標籤
全站熱搜
留言列表
