If the roots of the equation $12x^2 + mx + 5 = 0$ are in the ratio $3 : 2$,then $m = ......$

If $f(x)=ax^2+bx+c$ satisfies $f(1)+2f(2)=0$ and $2f(1)+f(2)=0$,then $3a+b=$

Let $\lambda \neq 0$ be a real number. Let $\alpha, \beta$ be the roots of the equation $14 x^2-31 x+3 \lambda=0$ and $\alpha, \gamma$ be the roots of the equation $35 x^2-53 x+4 \lambda=0$. Then $\frac{3 \alpha}{\beta}$ and $\frac{4 \alpha}{\gamma}$ are the roots of the equation :

If $\alpha, \beta, \gamma$ are the roots of $x^3+2x^2-3x-1=0$,then $\alpha^{-2}+\beta^{-2}+\gamma^{-2}=$

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

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^{3}+4x+2=0$,then $\alpha^{3}+\beta^{3}+\gamma^{3}$ is equal to