The roots of the equation $3x^3+6x^2-2x-4=0$ are $\alpha$, $\beta$ and $\gamma$. Write down

Question

The roots of the equation $3x^3+6x^2-2x-4=0$ are $\alpha$, $\beta$ and $\gamma$. Write down the values of $\alpha+\beta+\gamma$, $\alpha\beta+\beta\gamma+\gamma\alpha$ and $\alpha\beta\gamma$. Hence find the value of $\dfrac{1}{\alpha}+\dfrac{1}{\beta}+\dfrac{1}{\gamma}$.

Accepted Answer

(a) $-2,\ -\frac{2}{3},\ \frac{4}{3}$ (b) $-\frac{1}{2}$

Reciprocal sum for a cubic

Reciprocal sum for a cubic

Solution:

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