If ${x^2} + ax + 10 = 0$ and ${x^2} + bx - 10 = 0$ have a common root,then ${a^2} - {b^2}$ is equal to

The quadratic equations $x^2-6x+a=0$ and $x^2-cx+6=0$ have one root in common. If the other roots of the first and second equations are integers and are in the ratio $4:3$,then their common root is

Let $p_1(x) = x^3 - 2020x^2 + b_1x + c_1$ and $p_2(x) = x^3 - 2021x^2 + b_2x + c_2$ be polynomials having two common roots $\alpha$ and $\beta$. Suppose there exist polynomials $q_1(x)$ and $q_2(x)$ such that $p_1(x)q_1(x) + p_2(x)q_2(x) = x^2 - 3x + 2$. Then the correct identity is

If the equations $x^2 + bx - 1 = 0$ and $x^2 + x + b = 0$ have a common root different from $-1$,then $|b|$ is equal to

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 $x^2+ax+b=0$ and $x^2+bx+a=0$ $(a \neq b)$ have a common root,then $a+b$ is equal to