Solution:-let $\alpha,\beta,\gamma,\delta$ be the roots of equation.
It is given that,$\alpha+\beta=0$
and,$\alpha+\beta+\gamma+\delta=3/6=1/2$,this implies $\gamma+\delta=1/2$
and $(\alpha+\beta)(\gamma+\delta)+\alpha\beta+\gamma\delta=8/6=4/3$,this implies $\alpha\beta+\gamma\delta=8/6=4/3$
From here how to proceed,please guide me.
Any suggestion is greatly appreciated.
Best Answer
If $\pm \alpha$ are roots, average the statements you know to get
$$6 \alpha^4 + 8 \alpha^2 + 2 = 0$$
which is quadratic in $\alpha^2$, and can be solved for $\alpha$. Now given $\pm \alpha$, the problem can be reduced to another quadratic.