SOLUTION: given that the equation x^2+(2-h)x+h=0 has non-zero roots which differ by 2,find the value of (a)each root (b)h Thanks~~

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Question 457942: given that the equation x^2+(2-h)x+h=0 has non-zero roots which differ by 2,find the value of
(a)each root
(b)h
Thanks~~
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let r be one one of the roots. Then the other root is r - 2.
Then r(r - 2) = h, and r + r -2 = -(2-h) = h - 2.
The second equation gives 2r = h. Combining this with the 1st equation, we get
r(r - 2) = 2r.
==> r%5E2+-+2r+=+2r ==> r%5E2+-+4r+=+0, or r(r - 4) = 0.
==> r = 0, or r = 4. Reject r = 0 because of the given hypothesis. Thus one root is 4, and the other root is 2. The value of h is 2r, or h = 8.