Let $[r]$ denote the largest integer not exceeditio $r$ and the roots of the equation $3 x^2+6 x+5+\alpha\left(x^2+2 x+2\right)=0$ are complex number when ever $\alpha>L$ and $\alpha

For any real value of $x$. If $\frac{11 x^2+12 x+6}{x^2+4 x+2} \notin(a, b)$, then the value $x$ for which $\frac{11 x^2+12 x+6}{x^2+4 x+2}=b-a+3$ 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 $\alpha$ and $\beta$ are two double roots of $x^2+3(a+3) x-9 a=0$ for different values of $a(\alpha>\beta)$, then the minimum value of $x^2+\alpha x-\beta=0$ is