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

For $0 < c < b < a$,let $(a+b-2c)x^2 + (b+c-2a)x + (c+a-2b) = 0$ and $\alpha \neq 1$ be one of its roots. Then,among the two statements:
$(I)$ If $\alpha \in (-1, 0)$,then $b$ cannot be the geometric mean of $a$ and $c$.
$(II)$ If $\alpha \in (0, 1)$,then $b$ may be the geometric mean of $a$ and $c$.

If the equation whose roots are $p$ times the roots of the equation $x^4-2ax^3+4bx^2+8ax+16=0$ is a reciprocal equation,then $|p|=$ :

Given the equation $4x^2 + 4(a - 1)x + (1 - 2a) = 0$ has roots $\sin \theta$ and $\cos \theta$ $(0 < \theta < \frac{\pi}{2})$,then the maximum value of $(a + \sin \theta)$ 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

The number of integers $a$ in the interval $[1, 2014]$ for which the system of equations $x+y=a$ and $\frac{x^2}{x-1}+\frac{y^2}{y-1}=4$ has finitely many solutions is