The roots of the equation $2x^3-8x^2+3x+5=0$ are $\alpha$, $\beta$ and $\gamma$. Write down

Question

The roots of the equation $2x^3-8x^2+3x+5=0$ 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 $\alpha^2+\beta^2+\gamma^2$.

Accepted Answer

(a) $4,\ \frac{3}{2},\ -\frac{5}{2}$ (b) $13$

Root sums and products of a cubic

Root sums and products of a cubic

Solution:

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