91Ó°ÊÓ

Find the range of the function \(f(x)=\frac{x^{2}-x+1}{x^{2}+x+1}\).

Show that the expression \(\frac{p x^{2}+3 x-4}{p+3 x-4 x^{2}}\) will be capable of all real values when \(x\) is real, provided that \(p\) has any value between 1 and 7 .

Let \(c\) be a fixed real number. Show that a root of the polynomial \(P(x)=x(x+1)(x+2) \cdots \cdots(x+2009)-c\) can have multiplicity at most 2 .