Question 1128224: If (sqrt 3 - 1) is a root of the equation 2x^2-2kx+4 = 0, then k equals... Found 3 solutions by ikleyn, josmiceli, MathTherapy:Answer by ikleyn(52787) (Show Source):
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 = .
You can put this solution on YOUR website! Let the roots be and
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Let
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get another opinion, too. This is hard to prove.
