@Aditya Parson
–
No way!!. You can use the fact that the sum of roots of any equation is equal to the coefficient of the (highest-1)th power divided by the coefficient of the first term.
Now, we see in this expression that the roots are (1,2,3,4,....1001).
Hence the sum of the roots will be 1+2+3+4....+1001.
=((1001)*(1002))/2 = 501501.
hence

501501 = (-1)*(coefficient of x^1000)/(coefficient of x^1001)
Also we see that the coefficient of the highest power term (x^1001) will be 1.
Hence,

501501 = (-1)(Coefficient of x^1000)/1
=> coefficient of x^1000 = -501501*. :)
–
Saurabh Dubey
·
4 years, 3 months ago

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@Saurabh Dubey
–
Thanks, I didn't know that.
But the sum of roots of any equation is that equation?
Let us take \(x^2+2x+1\) The sum of it's roots is \((-2).\)
But according to your equation it should come as \(2\).
So did you mean or forgot to mention absolute value?
–
Aditya Parson
·
4 years, 3 months ago

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@Aditya Parson
–
Vieta's fomula's alternate between positive and negative for each coefficient. So his answer is wrong. It should be negative.
–
Bob Krueger
·
4 years, 3 months ago

## Comments

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TopNewestI'am getting the answer as -501501. I worked it out. (Edited after correction from Bob) – Saurabh Dubey · 4 years, 3 months ago

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– Bob Krueger · 4 years, 3 months ago

It's actually -501501. Alternate the sign.Log in to reply

– Saurabh Dubey · 4 years, 3 months ago

Oh! I totally forgot that.Thanks for the correction :)Log in to reply

– Aditya Parson · 4 years, 3 months ago

Did you use expansion?Log in to reply

501501 = (-1)*(coefficient of x^1000)/(coefficient of x^1001) Also we see that the coefficient of the highest power term (x^1001) will be 1. Hence,

501501 = (-1)

(Coefficient of x^1000)/1 => coefficient of x^1000 =-501501*. :) – Saurabh Dubey · 4 years, 3 months agoLog in to reply

– Aditya Parson · 4 years, 3 months ago

Thanks, I didn't know that. But the sum of roots of any equation is that equation? Let us take \(x^2+2x+1\) The sum of it's roots is \((-2).\) But according to your equation it should come as \(2\). So did you mean or forgot to mention absolute value?Log in to reply

– Bob Krueger · 4 years, 3 months ago

Vieta's fomula's alternate between positive and negative for each coefficient. So his answer is wrong. It should be negative.Log in to reply

– Saurabh Dubey · 4 years, 3 months ago

Ya Bob is right.Log in to reply