If $x^2+3x-2k=0$ and $x^2-2x-7k=0$ have a non-zero common root,then the positive root of the equation $kx^2+(k+2)x-(k+1)=0$ is

The common roots of the equations $x^{12} - 1 = 0$ and $x^4 + x^2 + 1 = 0$ are:

If $\alpha$ is the common root of the quadratic equations $x^2-5x+4a=0$ and $x^2-2ax-8=0$,where $a \in R$,then the value of $\alpha^4-\alpha^3+68$ is

If $x^2+5ax+6=0$ and $x^2+3ax+2=0$ have a common root,then that common root is

If the value of real number $a > 0$ for which $x^2 - 5ax + 1 = 0$ and $x^2 - ax - 5 = 0$ have a common real root is $\frac{3}{\sqrt{2\beta}}$,then $\beta$ is equal to

Let $\alpha$ be a common root of the equations $x^3-2x-25\lambda=0$ and $3x^3-8x-\frac{175}{3}\lambda=0$,where $\lambda > 0$. Then $\lambda=$