The polynomial $2x^3 + 6x^2 - 7x - 10$ has zeros $\alpha$, $\beta$ and $\gamma$ - HSC - SSCE Mathematics Extension 1 - Question 4 - 2018 - Paper 1

To find the value of $\alpha \beta \gamma(\alpha + \beta + \gamma)$, we can use Vieta's formulas, which relate the coefficients of the polynomial to the sums and products of its roots.

1. The polynomial can be represented as:

   $2x^3 + 6x^2 - 7x - 10 = 0$

   Here, the leading coefficient is 2, and we can extract the sums and products of the roots:

   • The sum of the roots: $\alpha + \beta + \gamma = -\frac{b}{a} = -\frac{6}{2} = -3$
   • The product of the roots: $\alpha \beta \gamma = -\frac{d}{a} = -\frac{-10}{2} = 5$.

2. Now we can substitute these values into the expression we want to evaluate:

   $\alpha \beta \gamma (\alpha + \beta + \gamma) = 5 \cdot (-3) = -15$

Thus, the correct answer from the given options is: B. -15.