If $\frac{k}{kx+3}+\frac{3}{3x-k}=\frac{12x+5}{(kx+3)(3x-k)}$ for all $x \in R - \{-\frac{3}{k}, \frac{k}{3}\}$,then both the roots of the equation $kx^2-7x+3=0$ are

If $(2-i)$ is one of the roots of the equation $x^4-9x^3+31x^2-49x+30=0$ and $\alpha, \beta$ $(\alpha < \beta)$ are its real roots,then $2\alpha-\beta=$

If $3$ is a root of $x^2+kx-24=0$,then it is also a root of which of the following equations?

The value of $\lambda$ such that the sum of the squares of the roots of the quadratic equation $x^2 + (3 - \lambda)x + 2 = \lambda$ has the least value is

The solution set of $8x \equiv 6 \pmod{14}$,$x \in \mathbb{Z}$,is

Let $\alpha, \beta$ be the roots of the equation $x^{2}-\sqrt{2}x+\sqrt{6}=0$ and $\frac{1}{\alpha^{2}}+1, \frac{1}{\beta^{2}}+1$ be the roots of the equation $x^{2}+ax+b=0$. Then the roots of the equation $x^{2}-(a+b-2)x+(a+b+2)=0$ are...