If $\alpha$, $\beta$ are zeroes of the polynomial $p(x) = 5x^2 - 6x + 1$, then find the value of $\alpha + \beta + \alpha\beta$.

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Accepted Answer

Step 1: $\alpha + \beta = \frac{6}{5}$
Step 2: $\alpha\beta = \frac{1}{5}$
Step 3: $\alpha + \beta + \alpha\beta = \frac{6}{5} + \frac{1}{5} = \frac{7}{5}$

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