If $x$ is real,then the maximum and minimum values of the expression $\frac{x^2 - 3x + 4}{x^2 + 3x + 4}$ are

If $x$ is real,then the sum of the maximum and the minimum values of the expression $\frac{x^2+4x+1}{x^2+x+1}$ is

If both roots of the quadratic equation $x^2 + (\sin \theta + \cos \theta)x + \frac{3}{8} = 0$ are positive and distinct,then the complete set of values of $\theta$ in $[0, 2\pi]$ is:

If $m$ is chosen in the quadratic equation $(m^2 + 1)x^2 - 3x + (m^2 + 1)^2 = 0$ such that the sum of its roots is greatest,then the absolute difference of the cubes of its roots is

If an angle $A$ of a $\Delta ABC$ satisfies $5 \cos A + 3 = 0$,then the roots of the quadratic equation $9x^2 + 27x + 20 = 0$ are

Let $\alpha, \beta$ be the roots of the equation $x^{2}-4 \lambda x+5=0$ and $\alpha, \gamma$ be the roots of the equation $x^{2}-(3 \sqrt{2}+2 \sqrt{3}) x+7+3 \lambda \sqrt{3}=0$. If $\beta+\gamma=3 \sqrt{2}$,then $(\alpha+2 \beta+\gamma)^{2}$ is equal to