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  4. For every x ∈ R, the polynomial x 8- x 5+ x 2- x +1 is -

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Q. For every $x \in R$, the polynomial $x ^8- x ^5+ x ^2- x +1$ is -

Complex Numbers and Quadratic Equations

Solution:

$x^5\left(x^3-1\right)+x(x-1)+1=y $
$ \text { when } x \geq 1 y >0 $
$ -1< x< 1 y >0 $
$x<-1 y>0 $
hence $y >0 $