If $\alpha^2 = 5\alpha - 3$ and $\beta^2 = 5\beta - 3$ where $\alpha \neq \beta$,what is the value of $\frac{\alpha}{\beta} + \frac{\beta}{\alpha}$?

If the roots of the given equation $2x^2 + 3(\lambda - 2)x + \lambda + 4 = 0$ are equal in magnitude but opposite in sign,then $\lambda = $

If $3p^2 = 5p + 2$ and $3q^2 = 5q + 2$,where $p \ne q$,then $pq$ is equal to

If $\alpha, \beta$ are the roots of $ax^2 + bx + c = 0$ and $\gamma, \delta$ are the roots of $px^2 + qx + r = 0$,and $D_1, D_2$ are their respective discriminants. If $\alpha, \beta, \gamma, \delta$ are in arithmetic progression,then $D_1 : D_2 = \dots$

If $\alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$,then the quadratic equation whose roots are $\alpha$ and $\beta$ is

If the roots of the equation $2x^2 - 3x + 5 = 0$ are the reciprocals of the roots of the equation $ax^2 + bx + 2 = 0$,then: