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

1. Identify Roots: From the polynomial $2x^3 + 6x^2 - 7x - 10$, Vieta's formulas tell us:

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

2. Calculate the Expression:
   Now substitute these values into the expression: $\alpha\beta\gamma(\alpha + \beta + \gamma) = 5 \cdot (-3) = -15.$

Thus, the required value of $\alpha\beta\gamma(\alpha + \beta + \gamma)$ is -15.
Given the options in the question, the correct answer is B: -15.