SOLUTION: 1. If {{{1/2}}} is one of the roots of the quadratic equation {{{kx^2-2kx+k-1=0}}}, find the value of {{{k}}}.
2. If {{{1/m}}} is one of the roots of the quadratic equation {{{m
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Question 705199: 1. If is one of the roots of the quadratic equation , find the value of .
2. If is one of the roots of the quadratic equation , find the value of
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Choosing #1 and abbreviating the solution process,
General solution to quadratic equation gives, after appropriate simplification steps, or . Now since one of the roots is 1/2, we should equate 1/2 to this expression for x (both of them just to be thorough) and try solving for k.
, and .
Either way ultimately gives k^2-4k=0,
,
and since k=0 does not have any use here, we choose k=4.
Our original quadratic equation could be amended for k=4 as,
.
...and if all was done well, one of the roots should be found to be 1/2
(but I did not yet actually check this).
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