If $p$ and $q$ are the roots of the equation $x^2 + pq = (p + 1)x$,then $q=$

The difference between two roots of the equation $x^3-13x^2+15x+189=0$ is $2$. Then the roots of the equation are:

The sum of the roots of a quadratic equation is $2$ and the sum of their cubes is $98$. Then the equation is:

If $\alpha, \beta, \gamma$ are the roots of the cubic equation $x^3+p_1 x^2+p_2 x+p_3=0$. Let $S_r=\alpha^r+\beta^r+\gamma^r$. Given $S_1=10, S_2=38$ and $S_3=-1840$,then $p_3=$

If $\alpha_1, \alpha_2$ and $\beta_1, \beta_2$ are the roots of the equations $ax^2 + bx + c = 0$ and $px^2 + qx + r = 0$ respectively,and the system of equations $\alpha_1 y + \alpha_2 z = 0$ and $\beta_1 y + \beta_2 z = 0$ has a non-zero solution,then:

If $p$ and $q$ are the roots of the equation $x^{2}+px+q=0$, then: