For what value of $a$ is the difference of the roots of the equation $2x^2 - (a + 1)x + (a - 1) = 0$ equal to their product?

The value of $p$ for which the sum of the squares of the roots of the equation $x^2 - (p + 3)x + (5p - 2) = 0$ assumes its least value is:

If one root of the cubic equation $x^3-7x^2+36=0$ is double of another,then the number of negative roots is

If the roots of the equation $lx^2 + nx + n = 0$ are in the ratio $p:q$,then $\sqrt{\frac{p}{q}} + \sqrt{\frac{q}{p}} + \sqrt{\frac{n}{l}} = $

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

Let $\lambda \neq 0$ be in $\mathbb{R}$. If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-x+2\lambda=0$ and $\alpha$ and $\gamma$ are the roots of the equation $3x^{2}-10x+27\lambda=0$,then $\frac{\beta\gamma}{\lambda}$ is equal to