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 $p_1(x) = x^3 - 2020x^2 + b_1x + c_1$ 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

The equations $2x^2+ax-2=0$ and $x^2+x+2a=0$ have exactly one common root. If $a \neq 0$,then one of the roots of the equation $ax^2-4x-2a=0$ is

If $\alpha$ is a common root of $x^2-5x+\lambda=0$ and $x^2-8x-2\lambda=0$ $(\lambda \neq 0)$ and $\beta, \gamma$ are the other roots of them respectively,then $\alpha+\beta+\gamma+\lambda=$

Let $a \ne b, c \ne 0$. If the equations $x^2 + ax + bc = 0$ and $x^2 + bx + ac = 0$ have a common root,then:
Statement-$1$: The equation of the other roots is $x^2 + cx + ab = 0$.
Statement-$2$: $a + b + c = 0$.

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: