If the product of the roots of $9x^3 + 112x^2 - 120x + a = 0$ is $12$,then the value of '$a$' is

If the roots of the equation $ax^2 + bx + c = 0$ are $\sin \alpha$ and $\cos \alpha$,then:

If the roots of the equation $(x - a)(x - b) = c$ (where $c \neq 0$) are $\alpha$ and $\beta$,then what are the roots of the equation $(x - \alpha)(x - \beta) + c = 0$?

If the sum of two of the roots of $x^3+p x^2-q x+r=0$ is zero,then $pq$ is equal to

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 4x + 1 = 0$,the value of $\alpha^3 + \beta^3$ is:

Two students were solving a quadratic equation in $x$. One student copied the constant term incorrectly and obtained the roots $3$ and $2$. The other student copied the constant term and the coefficient of $x^2$ correctly as $-6$ and $1$ respectively. What are the correct roots?