If $\alpha, \beta,\gamma$ are the roots of $x^3+4x+1=0,$ then the equation whose roots are $\large\frac{\alpha^2}{\beta +\gamma},\frac{\beta^2}{\gamma+\alpha},\frac{\gamma^2}{\alpha+\beta}$ is :

Question

\[\begin {array} {1 1} (1)\;x^3-4x-1=0 & \quad (2)\;x^3-4x+1=0 \\ (3)\;x^3+4x-1=0 & \quad (4)\;x^3+4x+1=0 \end {array}\]

Answer 1

(3) $x^3+4x-1=0$