Let \( \Large \alpha \) and \( \Large \beta \) be the roots of the

quadratic equation \( \Large 2x^{2} - 11x + 5 = 0 \)

Therefore, \( \Large \alpha + \beta = - \frac{ \left(-11\right) }{2} = \frac{11}{2} \)

and \( \Large \alpha . \beta = \frac{5}{2} \)

Now, 

= \( \Large \left(\frac{11}{2}\right)^{2} - 4 \left(\frac{5}{2}\right) = \frac{121}{4} - \frac{20}{2} \)

= \( \Large \frac{121 - 4}{4} = \frac{51}{4} = \left(\frac{9}{2}\right)^{2} \)

Therefore, Difference of roots = \( \Large \left( \alpha - \beta \right) = \frac{9}{2} = 4.5 \)