SOLUTION: If one root of the equation X^2+K(3K-5x)=1-2K is four time than other,find the value of k Thanks~~

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Question 456977: If one root of the equation X^2+K(3K-5x)=1-2K is four time than other,find the value of k
Thanks~~
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let r be one root of the equation. Then the other root must be 4r.
==> (x - r)(x - 4r) = 0 <==> x%5E2+-+5rx+%2B+4r%5E2+=+0
Now the given equation is equivalent x%5E2+-+5kx+%2B%283k%5E2+%2B+2k+-+1%29+=+0 after rearrangement of terms.
==> -5k = -5r, or k = r, after direct comparison of coefficients.
==> 3k%5E2+%2B+2k+-+1+=+4r%5E2+=+4k%5E2, or
0+=+k%5E2+-+2k+%2B+1+=+%28k-1%29%5E2, or k = 1.