If the equations $x^2 + px + q = 0$ and $x^2 + qx + p = 0$ have a common root,then $p + q + 1 = $

The equations $5x^2 + 12x + 13 = 0$ and $ax^2 + bx + c = 0$ have a common root,where $a, b, c$ are the sides of $\Delta ABC$. Find $\angle C$ in degrees.

Let $a, b, c, d \in \mathbb{R}$. If the equations $2bx^2 + 3cx - d = 0$ and $2ax^2 + 3bx + 4c = 0$ have a common root and $\frac{4bc + ad}{k(b^2 - ac)} = \frac{bd + 4c^2}{4bc + ad}$,then $k =$

If the quadratic equations $x^2 - 7x + 3c = 0$ and $x^2 + x - 5c = 0$ have a common root,then for a non-zero real value of $c$,the sign of the expression $x^2 - 3x + c$ is:

If the quadratic equations $3x^2 + ax + 1 = 0$ and $2x^2 + bx + 1 = 0$ have a common root,then what is the value of the expression $5ab - 2a^2 - 3b^2$?

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