1. Determine all values of the parameter $m$ such that for every $x$ the following holds

$$
\left(4 m^{2}-5 m+1\right) x^{2}+2(m+1) x+1>0
$$
The inequality $a x^{2}+b x+c>0$ holds for every real number $x$ if and only if $a>0$ and $D=b^{2}-4 a c<0$. From $a>0$ it follows that $m \in\left(-\infty,-\frac{1}{4}\right) \cup(1,+\infty)$, and from $D<0$, it follows that $m \in(-\infty, 0) \cup\left(\frac{7}{3},+\infty\right)$, i.e., the inequality (1) holds for every real number $x$ if and only if $m \in(-\infty, 0) \cup\left(\frac{7}{3},+\infty\right)$