If $\text{'}\mathrm{\alpha }\text{'} \mathrm{and} \text{'}\mathrm{\beta }\text{'}$ be the lengths of the line segment of any focal chord of parabola ${\mathrm{y}}^2=4\mathrm{ax}$ where $\mathrm{\alpha }, \mathrm{\beta }$ are the roots of the equation $\left(5+\sqrt{2}\right){\mathrm{x}}^2-\left(4+\sqrt{5}\right)\mathrm{x}+\left(4+\sqrt{5}\right)=0$

then the length of the Semi latusrectum of the parabola is