Real polynomial/Positive/Estimate/Exercise

Let

${}P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{2}x^{2}+a_{1}x+a_{0}\,$

denote a real polynomial with ${}a_{n}>0$. Describe in dependence on the coefficients ${}a_{0},\ldots ,a_{n}$ a bound ${}b$ such that

${}P(x)>0\,$

holds for all ${}x\geq b$.

Create a solution