Description for Correct answer:
\( \Large 2\sin^{2}\frac{ \pi }{8}=1-\cos \frac{ \pi }{4}=1-\frac{1}{\sqrt{2}}=\frac{\sqrt{2-1}}{\sqrt{2}} \)

(irrational root) so, other roots \( \Large \frac{\sqrt{2}+1}{\sqrt{2}} \)

Sum of roots \( \Large -a = 1-\frac{1}{\sqrt{2}}+1+\frac{1}{\sqrt{2}}=2 => a = -2 \)

products of roots \( \Large 1-\frac{1}{2} = \frac{1}{2} = b \)

so, \( \Large a-b = -2-\frac{1}{2} = -\frac{5}{2} \)