Question

if alpha and beta are zeros of a quadratic polynomial f(x)=ax2+bx+c,then evaluate1/aalpha+b +1/abeta=b

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ {\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0 \\ \mathrm{So}\mathrm{\alpha }+\mathrm{\beta }=\frac{-\mathrm{b}}{\mathrm{a}} \\ \mathrm{\alpha \beta }=\frac{\mathrm{c}}{\mathrm{a}} \\ \mathrm{Now}, \\ \frac{1}{\mathrm{\alpha }}+\frac{1}{\mathrm{\beta }}+\mathrm{b}=\frac{\mathrm{\alpha }+\mathrm{\beta }}{\mathrm{\alpha \beta }}+\mathrm{b} \\ =\frac{{\displaystyle \frac{-\mathrm{b}}{\mathrm{a}}}}{{\displaystyle \frac{\mathrm{c}}{\mathrm{a}}}}+\mathrm{b}=\frac{-\mathrm{b}}{\mathrm{c}}+\mathrm{b} \\ \mathrm{Regards} \end{gathered}$$