Given $P\left(x\right)=x^4+a{x}^3+b{x}^2+cx+d$ such that$x=0$ $P\text{'}\left(x\right)=0$ is the only real root of. If $P\left(-1\right)<P\left(1\right)$, then in the interval$\left[-1,1\right]$:

Assertion $\left(A\right): 3x^2-16x+4>-16$ is satisfied for some values of real $x$ in $\left(0,\frac{10}{3}\right)$. 

Reason $\left(R\right): a{x}^2+bx+c$ and $a$ will have the same sign for some values of $x\in R$ when $b^2-4ac>0$. 

The correct option among the following is

If $x\in R$ then determine the range of the expression $\frac{x^2+x+1}{x^2-x+1}$.