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

Question

If $\alpha, \beta$ are the zeroes of a polynomial $p(x)=x^{2}+x-1$, then $\frac{1}{\alpha}+\frac{1}{\beta}$ equals to\

Professor PC Thomas Classes · Answer

(a): We have, $p(x)=x^{2}+x-1, \alpha+\beta=-1$\ and $\alpha \beta=-1$\ Now, $\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}=\frac{-1}{-1}=1$\