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If alpha and beta are the roots of ax^2+...

If `alpha` and `beta` are the roots of `ax^2+bx+c=0`, then the equation `ax^2-bx(x-1)+c(x-1)^2=0` has roots

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As `alpha` and `beta` are the roots of `ax^2+bx+c = 0`.
`:. alpha+beta = -b/a and alphabeta = c/a`
Now, second equation is,
`ax^2-bx(x-1)+c(x-1)^2 = 0`
`=>(a-b+c)x^2-x(b-2c)+c = 0`
Let `m` and `n` are the roots of this equation.
Then, `mn = c/(a-b+c) = (c/a)/(1-b/a+c/a)`
`=(alpha beta)/(1+(alpha+beta)+alpha beta)`
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