For the given quadratic equation x² − 4x + 2 = 0, the sum of the roots is alpha + beta = -((-4))/(1) = 4, and the product of the roots is alphabeta = (2)/(1) = 2.

Here are the solutions to the remaining questions.

1d) If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 4x + 2 = 0$, find the equation whose roots are $\alpha + \frac{1}{\beta}$ and $\beta + \frac{1}{\alpha}$.

Step 1: For the given quadratic equation $x^2 - 4x + 2 = 0$, the sum of the roots is $\alpha + \beta = -\frac{(-4)}{1} = 4$, and the product of the roots is $\alpha\beta = \frac{2}{1} = 2$.

Step 2: Find the sum of the new roots, $S'$.

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