SOLUTION: If (√3 - 1) is a root of the equation 2x^2-2kx+4 = 0, then k equals... A)2√3-1 B)√3-2 C)2√3 D)√3 E)√3-1

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Question 1128329: If (√3 - 1) is a root of the equation 2x^2-2kx+4 = 0, then k equals...
A)2√3-1 B)√3-2 C)2√3 D)√3 E)√3-1
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
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 = .

Solved.   //   Option C).



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