Calculate the 2015 roots!

Algebra Level 2

x 2015 = 2015 x^{2015}=2015

What is the sum of all the roots of the equation?


The answer is 0.

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2 solutions

Mehul Arora
Aug 3, 2015

x 2015 2015 = 0 x^{2015}-2015=0

B Vieta's, The sum of all roots = ( c o e f f i c i e n t o f t h e s e c o n d t e r m ) c o e f f i c i e n t o f t h e f i r s t t e r m \dfrac {-(coefficient \ of \ the \ second \ term)}{coefficient \ of \ the \ first \ term}

0 1 = 0 \Rightarrow \dfrac {0}{1}=0

Umm, shouldn't it be 1 1 in the denominator, instead of 2015 2015 ....??

A Former Brilliant Member - 5 years, 10 months ago

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Ohh, thanks for noticing! Careless errors :P

Thanks @Abhineet Nayyar :D

Mehul Arora - 5 years, 10 months ago

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No worries, and welcome back @Mehul Arora

A Former Brilliant Member - 5 years, 10 months ago

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@A Former Brilliant Member Thanks! :D

Mehul Arora - 5 years, 10 months ago

Hey...doesn't that happen in quadratic equations...

Tanisha Ghosh - 5 years, 8 months ago

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Hi Tanisha! Actually, it happens in all the equations. This is called (Vieta's formula)[https://brilliant.org/wiki/vietas-formula/]

Mehul Arora - 5 years, 8 months ago
Mohit Gupta
Aug 3, 2015

Pretty easy question as the coefficient of second term is ZERO therefore -b/a=0

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