If the equations $x^2 + ax + 10 = 0$ and $x^2 + bx - 10 = 0$ have a common root,then $a^2 - b^2 = \dots \dots$

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 $3x^2 - 7x + 2 = 0$ and $15x^2 - 11x + a = 0$ have a common root and $a$ is a positive real number,then the sum of the roots of the equation $15x^2 - ax + 7 = 0$ is:

If the two equations $x^2 - cx + d = 0$ and $x^2 - ax + b = 0$ have one common root and the second equation has equal roots,then $2(b + d) = $

If $2x^2+3x-2=0$ and $3x^2+ax-2=0$ have one common root,then the sum of all possible values of $a$ is (in $.5$)

Let $\lambda \neq 0$ be in $\mathbb{R}$. If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-x+2\lambda=0$,and $\alpha$ and $\gamma$ are the roots of the equation $3x^{2}-10x+27\lambda=0$,then $\frac{\beta\gamma}{\lambda}$ is equal to: