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?

If $\alpha, \beta$ are the roots of $x^2-5 \gamma x-6 \delta=0$ and $\gamma, \delta$ are the roots of $x^2-5 \alpha x-6 \beta=0$,then $\alpha+\beta+\gamma+\delta=$

If the roots of the quadratic equation $x^2 + px + q = 0$ are $\tan 30^\circ$ and $\tan 15^\circ$ respectively,then the value of $2 + q - p$ is

If the coefficients of the equation whose roots are $k$ times the roots of the equation $x^3+\frac{1}{4} x^2-\frac{1}{16} x+\frac{1}{144}=0$ are integers,then a possible value of $k$ is

The cubic equation whose roots are the squares of the roots of the equation $12x^3-20x^2+x+3=0$ is

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