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the number of real roots of the equation:- 2x^2015 +3x^2014 +2x^2013 +3x^2012 +................+2x+3=0.

the number of real roots of the equation:-
2x^2015 +3x^2014 +2x^2013 +3x^2012 +................+2x+3=0.

Grade:Select Grade

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
8 years ago
This equation can be factorized as
2x(x^{2014}+x^{2012} + ... + 1) + 3(x^{2014}+x^{2012} + ... + 1) = 0
(2x+3)(x^{2014}+x^{2012} + ... + 1) = 0

so one root is -3/2
and the remaining factor is always positive and hence have no real root
so the equation has only one real root

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