Find all the values of the parameter $a$ for which both roots of the quadratic equation ${ x }^{ 2 }-ax+2=0$ belong to the interval $\left( 0,3 \right) $.

For both roots of $x^2 - ax + 2 = 0$ to be in the interval $(0,3)$, three conditions must be met: the sum of the roots $a$ must be greater than $2\sqrt{2}$ (from the arithmetic mean-geometric mean inequality on roots with product $2$), the value of the polynomial at $x=3$ must be positive, and the axis of symmetry must be within the interval. Evaluating at $x=3$ gives $9 - 3a + 2 > 0$, which simplifies to $a < 11/3$. Combining these requirements gives the range $2\sqrt{2} < a < 11/3$.

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