The roots of the equation $3x^2+5x-2=0$ are $\alpha$ and $\beta$. Without solving the equation

Question

The roots of the equation $3x^2+5x-2=0$ are $\alpha$ and $\beta$. Without solving the equation, find the value of each of the following. $\alpha^2\beta+\alpha\beta^2$ $\dfrac{1}{\alpha^2}+\dfrac{1}{\beta^2}$

Accepted Answer

(a) $\frac{10}{9}$ (b) $\frac{37}{4}$

Symmetric products with squared factors

Symmetric products with squared factors

Solution:

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