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
–
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?

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TopNewestI'am getting the answer as -501501. I worked it out. (Edited after correction from Bob)

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It's actually -501501. Alternate the sign.

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Oh! I totally forgot that.Thanks for the correction :)

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Did you use expansion?

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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*. :)Log in to reply

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