Question

If alpha and beta are the zeros of the polynomial 4 x square + 3 X + 7 then find the value of one by Alpha Plus One by beta

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{p}\left(\mathrm{x}\right)=4{\mathrm{x}}^2+3\mathrm{x}+7 \\ \mathrm{Now},\mathrm{\alpha }+\mathrm{\beta }=-\frac{\mathrm{coefficient}\mathrm{of}\mathrm{x}}{\mathrm{coefficient}\mathrm{of}{\mathrm{x}}^2}=-\frac{3}{4} \\ \mathrm{Now},\mathrm{\alpha \beta }=\frac{\mathrm{constant}\mathrm{term}}{\mathrm{coefficient}\mathrm{of}{\mathrm{x}}^2}=\frac{7}{4} \\ \mathrm{Now},\frac{1}{\mathrm{\alpha }}+\frac{1}{\mathrm{\beta }} \\ =\frac{\mathrm{\beta }+\mathrm{\alpha }}{\mathrm{\alpha \beta }} \\ =\frac{-3/4}{7/4} \\ =-\frac{3}{7} \end{gathered}$$