$4+\frac{1}{4+\frac{1}{4+\frac{1}{4+\ldots \infty}}} = $

If the difference of the roots of the equation $x^2-7x+10=0$ is same as the difference of the roots of the equation $x^2-17x+k=0$,then a divisor of $k$ is

If for some $p, q, r \in \mathbb{R}$,not all have the same sign,and one of the roots of the equation $(p^{2}+q^{2})x^{2}-2q(p+r)x + q^{2}+r^{2}=0$ is also a root of the equation $x^{2}+2x-8=0$,then $\frac{q^{2}+r^{2}}{p^{2}}$ is equal to-

If $\alpha, \beta, \gamma, \delta, \varepsilon$ are the roots of the equation $x^5+x^4-13x^3-13x^2+36x+36=0$ and $\alpha < \beta < \gamma < \delta < \varepsilon$,then find the value of $\frac{\varepsilon}{\alpha}+\frac{\delta}{\beta}+\frac{1}{\gamma}$.

If $P(x) = ax^2 + bx + c$ and $Q(x) = -ax^2 + dx + c$ where $ac \neq 0$,then $P(x) \cdot Q(x) = 0$ has at least:

If the difference between the roots of the equations $x^2 - bx + c = 0$ and $x^2 - cx + b = 0$ is the same,then $b + c = \dots$