Question

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

• A. positive
• B. never positive
• C. positive as well as negative
• D. negative

Answer 1

Answer: (A)

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