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

Algebra ->  Quadratic Equations and Parabolas -> 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      Log On


   

Question 705199: 1. If 1%2F2 is one of the roots of the quadratic equation kx%5E2-2kx%2Bk-1=0, find the value of k.
2. If 1%2Fm is one of the roots of the quadratic equation mx%5E2%2B7x-2m=0, find the value of m
Answer by josgarithmetic(39618) About Me  (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, x=%28k%2Bsqrt%28k%29%29%2Fk or x=%28k-sqrt%28k%29%29%2Fk. 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.

1%2F2=%28k%2Bsqrt%28k%29%29%2Fk, and 1%2F2=%28k-sqrt%28k%29%29%2Fk.
Either way ultimately gives k^2-4k=0,
k%28k-4%29=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,
4x%5E2-2%2A4x%2B4-1=0
4x%5E2-8x%2B3=0
.
...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).