If $\alpha$ and $\beta$ are two zeroes of the quadratic polynomial ...

Question

If $\alpha$ and $\beta$ are two zeroes of the quadratic polynomial $p(x) = x^2 - 11x + 30$, then $\frac{1}{\alpha}+\frac{1}{\beta}$ is equal to:

Accepted Answer

For $p(x)=x^2-11x+30$: Sum of zeroes $\alpha+\beta = -\frac{-11}{1}=11$, Product $\alpha\beta = \frac{30}{1}=30$. $$\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}=\frac{11}{30}$$

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