If $\alpha ,{\beta }^2$  are roots of  $5x^2-20x+3k=0$ and $\beta ,{\alpha }^2$  are roots of  $k{x}^2-50x+45=0$
(a, b,  $\alpha ,\beta \in R$ and $k\ne 0,\alpha >\beta$ ), then which of the following option(s) is/are correct?
 

 $\alpha +{\beta }^2=4,\alpha {\beta }^2=\frac{3k}{5},\beta {\alpha }^2=\frac{45}{K}and\beta +{\alpha }^2=\frac{50}{k}\Rightarrow {\alpha }^3{\beta }^3=27,\alpha \beta =3$
 $\Rightarrow \alpha =3,\beta =1andk=5$
Since,   is root of  $5x^2-20x+3k=0$
 ${\beta }^4-4{\beta }^2+3=0$
 $\Rightarrow {\beta }^3-4\beta +\frac{3}{\beta }=0or{\beta }^3-4\beta +\alpha =0$
 ${\alpha }^4-10{\alpha }^2+9=0\Rightarrow {\alpha }^3-10\alpha +3\beta =0$