If $2\sin^{2}\dfrac {\pi}{8}$ is a root of the equation $x^{2} + ax + b = 0$, where $a$ and $b$ are rational numbers, then $a - b$ is equal to

The given root is 2 * sin^2(pi/8), which equals 1 - cos(pi/4) or 1 - 1/sqrt(2). Because a and b are rational, the other root must be the conjugate 1 + 1/sqrt(2). The sum of the roots is 2, so a = -2, and the product of the roots is 1 - 1/2 = 1/2, so b = 1/2. Therefore, a - b = -2 - 1/2 = -5/2.

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