Question 1113540: How do I determine the ratio of the roots of the equations Kx^(2)-x+1=0 x^(2)-x+k=0 ?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! One can find the roots of this equation by using the quadratic formula
x=(1/2a)(-b+/- sqrt(b^2-4ac), where a=K, b=-1, and c=1
The first way assumes K is the same as k
the first using the quadratic formula is x=(1/2k)(1+/- sqrt (1-4k))
the other is x=(1/k)(1+/- sqrt (1-4k))
The ratio is (1/2k)/(1/k) or 1/2, since the (1+/-sqrt (1-4k)) cancel
If the K is not the same as k
(1/2K)(1+/- sqrt (1-4k))/(1/k)(1+/- sqrt (1-4k))
and this ratio is (1/2K)/(1/k) as above, which is k/2K
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