The equation

    2x^2 - 2kx + 4 = 0 

is equivalent to  (after dividing both sides by 2)


    x^2 - kx + 2 = 0.      (1)


We are given that    is the root of the original equation; hence, the equation (1) with the leading coefficient 1 has this root, too.


Then, applying the Vieta's theorem, the other root of the equation (1) is


     = . =  =  = .


Thus we know BOTH ROOTS of the equation (1) (even without solving it explicitly (!) ). They are


      and  .


Again, according to Vieta's theorem, the sum of these roots is the coefficient at x in equation (1) taken with the opposite sign:


    k =  +  = .


Answer.  k = .

 

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