If $\alpha, \beta$ are the zeroes of the polynomial $p(x) = x^2-3x-...

Question

If $\alpha, \beta$ are the zeroes of the polynomial $p(x) = x^2-3x-1$, then find the value of $\frac{1}{\alpha}+\frac{1}{\beta}$.

Accepted Answer

For $p(x) = x^2-3x-1$, comparing with $ax^2+bx+c$: sum of zeroes $\alpha+\beta = -\frac{b}{a} = 3$, product of zeroes $\alpha\beta = \frac{c}{a} = -1$. $\frac{1}{\alpha}+\frac{1}{\beta} = \frac{\alpha+\beta}{\alpha\beta} = \frac{3}{-1} = -3$.

🔔 Email Updates Lein