1
$\begingroup$

What is the sum of the roots of the equation

$$(x − 1) + (x − 2)^2 + (x − 3)^3 + ... + (x − 10)^{10} = 0 $$?

When i expand this equation, it become in the power of 10 and its get complicated. Now what i am thinking is the sum of roots will be equal to the sum of coefficents of x^9 .So i just need to evaluate coefficent of x^9 in the term $$(x-10)x^{10}$$. Am in right in thinking?

But is there is any other easier way by which i can calculate?

Thanks in advance.

  • 3
    Yes, you are right. Take a look at: http://en.wikipedia.org/wiki/Vieta's_formulas2012-04-16
  • 2
    I would think you'd be after the coeff of $x^9$ in $(x-9)^9+(x-10)^{10}$.2012-04-16
  • 0
    Ya,I dint mention it as the coefficent of x^9 in (x-9)^9 will be 1 for sure.2012-04-16

2 Answers 2