IIT JEE , AIEEE Forum - Mathematics , Algebra

konichiwa2x

Well this is not a very different method, but anyway...

In general if

, are the roots of a polynomial

of degree n, then

this is very easy to see: let

then

now differentiate with respect to x to get the result. so, for example, if

,
then

, and

thus

ps. you can do this by another method, but its pretty tedious. You can look at the case e.g n=3 or n=4 and then generalize.Clear the denominators, simplify, and group on the left. using that sums of roots, products of pairs of roots, etc are -1,+1, -1 , + 1 etc from coefficients of P(x) combined with P(1) = n+1, you can prove it.

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