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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:
for $x \geq 1 E=x^5\left(x^3-1\right)+(x-1)+1 >0$
for $1< x< 0, E=(1-x)+x^2\left(1-x^3\right)+x^8 >0$
For $x < 0$, all terms are positive $\Rightarrow>0$ Hence $A$