Number of rational roots of equation x^{2016} -x^{2015} + x^{1008} + x^{1003} + 1 = 0, is equal to

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4-2.Quadratic Equations and Inequations

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Number of rational roots of equation $x^{2016} -x^{2015} + x^{1008} + x^{1003} + 1 = 0,$ is equal to

A

$0$

B

$1008$

C

$2015$

D

$2016$

Solution

Let $\mathrm{x}=\frac{\mathrm{p}}{\mathrm{q}}$ is a root, then $\mathrm{p}$ and $\mathrm{q}$ both are divisors of $1$

$\therefore $ ${p}, {q} \in\{-1,1\}$ but $f(-1) \neq 0, f(1) \neq 0$

so, equation has no rational roots.

Standard 11

Mathematics

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