The polynomial $x^3 + 2x^2 - 5x - 6$ has zeros $-1$, $-3$ and $\alpha$ - HSC - SSCE Mathematics Extension 1 - Question 1 - 2024 - Paper 1

According to Vieta’s formulas, the sum of the roots of a polynomial of the form $ax^3 + bx^2 + cx + d$ is given by $-\frac{b}{a}$. Here, $a = 1$ and $b = 2$. Thus, the sum of the roots is $-\frac{2}{1} = -2$.

Now, we can set up the equation with the known zeros: $-1 + (-3) + \alpha = -2$

Combining the known zeros: $-4 + \alpha = -2$ Solving for $\alpha$, we find: $\alpha = -2 + 4$ $\alpha = 2$

Therefore, the value of $\alpha$ is \textbf{2}, corresponding to option B in the multiple choice answers.