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

$\mathrm{\alpha }+\mathrm{\beta }=\frac{3}{2} \mathrm{and} \mathrm{\alpha \beta }=2$

${\mathrm{\alpha }}^2+{\mathrm{\beta }}^2={(\mathrm{\alpha }+\mathrm{\beta })}^2-2\mathrm{\alpha \beta }=\frac{9}{4}-4=-\frac{7}{4}$

Hence required equation ${\mathrm{x}}^2-({\mathrm{\alpha }}^2+{\mathrm{\beta }}^2)\mathrm{x}+{\mathrm{\alpha }}^2{\mathrm{\beta }}^2=0$

$\Rightarrow {\mathrm{x}}^2+\frac{7}{4}\mathrm{x}+4=0\Rightarrow 4{\mathrm{x}}^2+7\mathrm{x}+16=0$