Question

If alpha and beta are the zeros of the polynomial p x is equal to 2 X square + 3 X + 5 then find one upon alpha plus one upon beta

Answer 1

Dear student
$$\begin{gathered} Given: \\ p\left(x\right)=2x^2+3x+5 \\ Also,\alpha and\beta arerootsofp\left(x\right) \\ So, \\ \alpha +\beta =\frac{-coeff.ofx}{coeffof{x}^2}=\frac{-3}{2}...\left(1\right) \\ and\alpha \beta =\frac{cons\tan tterm}{coeff.of{x}^2}=\frac{5}{2}...\left(2\right) \\ Tofind:\frac{1}{\alpha }+\frac{1}{\beta } \\ =\frac{\alpha +\beta }{\alpha \beta } \\ =\frac{{\displaystyle \frac{-3}{2}}}{\frac{5}{2}}\left[u\sin g\left(1\right)and\left(2\right)\right] \\ =\frac{-3}{5} \\ So,\boxed{\mathbf{}\frac{\mathbf{1}}{\mathbf{\alpha }}\mathbf{+}\frac{\mathbf{1}}{\mathbf{\beta }}\mathbf{=}\frac{\mathbf{-}\mathbf{3}}{\mathbf{5}}} \end{gathered}$$
Regards