If $p$ and $q$ are prime numbers satisfying the condition $p^{2}-2q^{2}=1$,then the value of $p^{2}+2q^{2}$ is

If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}$ is equal to

If $2 \sin^3 x + \sin 2x \cos x + 4 \sin x - 4 = 0$ has exactly $3$ solutions in the interval $[0, \frac{n \pi}{2}]$,$n \in N$,then the roots of the equation $x^2 + nx + (n-3) = 0$ belong to :

The sum of non-real roots of the polynomial equation $x^3+3x^2+3x+3=0$ is

The solution of the equation $\frac{p + q - x}{r} + \frac{q + r - x}{p} + \frac{r + p - x}{q} + \frac{3x}{p + q + r} = 0$ is

The roots of $ax^2 + b = 0$ are real and distinct if: