If $2, 3, 6$ are the roots of the polynomial $f(x) = x^3 + ax^2 + bx + c$,where $a, b, c \in \mathbb{C}$. Then,the value of $a - c$ is

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+ax^2+bx+c=0$,then the roots of the equation $x^3+(2b-a^2)x^2+(b^2-2ac)x-c^2=0$ are

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:

If the sum of the roots of the equation $ax^2 + bx + c = 0$ is equal to the sum of the reciprocals of their squares,then $bc^2, ca^2, ab^2$ will be in

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?

If $\alpha, \beta, \gamma$ are roots of $x^3-5x+4=0$,then $(\alpha^3+\beta^3+\gamma^3)^2$ is equal to