If $x$ is real, then the value of $\frac{x^2-3x+4}{x^2+3x+4}$ lies in the interval

For what condition will the expression $a^2x^2 + bx + 1$ be positive for all $x \in R$?

The number of ordered pairs $(a, b)$ of integers such that $a-b$ is a root of $x^2+ax+b=0$ is

If $\frac{5}{2}$ is the sum of two roots of the equation $6x^6-25x^5+31x^4-31x^2+25x-6=0$,then the sum of all non-real roots of the equation is

If the roots of $\sqrt{\frac{1-y}{y}}+\sqrt{\frac{y}{1-y}}=\frac{5}{2}$ are $\alpha$ and $\beta$ $(\beta > \alpha)$ and the equation $(\alpha+\beta) x^4-25 \alpha \beta x^2+(\gamma+\beta-\alpha)=0$ has real roots,then a possible value of $\gamma$ is

If $\frac{x^2+ax+3}{x^2+x+1}$ takes all real values for all real values of $x$,then $a$ lies in the interval