Given the quadratic equation 3x2 − 11x + 4 = 0, with roots alpha and beta.

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Question 9:
Given the quadratic equation $3x^2 - 11x + 4 = 0$, with roots $\alpha$ and $\beta$.
From the equation, we have:
Sum of roots: $\alpha + \beta = -\frac{(-11)}{3} = \frac{11}{3}$
Product of roots: $\alpha \beta = \frac{4}{3}$

We need to find the equation whose roots are $X_1 = \alpha^2 + \frac{1}{\beta}$ and $X_2 = \frac{1}{\alpha} + \beta^2$.

Step 1: Calculate the sum of the new roots, $S = X_