If $x^2 - hx - 21 = 0$ and $x^2 - 3hx + 35 = 0$ $(h > 0)$ have a common root,then the value of $h$ is equal to

For how many values $a \in \mathbb{C}$,do the equations $x^2-8x+7=0$ and $x^2-2ax+49=0$ have a common root?

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

The value of $a$ for which the equations $x^3+ax+1=0$ and $x^4+ax^2+1=0$ have a common root is

Let the equations $ax^2-7x+c=0$ and $ax^2+5x-c=0$ have a common root and $ac \neq 0$. If $3$ is a root of $ax^2-7x+c=0$ other than the common root,then the common root of the given equations is

If the equations $ax^2 + bx + a = 0$ and $x^3 - 2x^2 + 2x - 1 = 0$ have two common roots,then what is the value of $a + b$?