If a and b are the roots of the equation $x^{2}-3x+2=0,$ the $\dfrac{1}{a }+\dfrac{1}{b^{4}}$ is:

Using Vieta's formulas for the equation x^2 - 3x + 2 = 0, the sum of the roots is a + b = 3 and the product is ab = 2. The roots are clearly 1 and 2. Assuming the expression to evaluate is (1/a) + (1/b^4), we assign a = 1 and b = 2. Substituting these values gives (1/1) + (1/2^4) = 1 + 1/16 = 17/16. If the expression was meant to be symmetric, the result changes, but based on the exact notation provided, the value is 17/16.

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