F4 A.maths (Quadratic equation)

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