Sum of root of equation \(=a+\beta\)
\(=\frac{-1}{a}=\frac{-(-5)}{1}=5\)
product of root of equation.
\((\alpha \beta)=\frac{c}{a}=4\)
\(\frac{1}{\alpha}-\frac{1}{\beta}: \frac{\beta-\alpha}{\alpha \beta}=\frac{-(\alpha-\beta)}{\alpha \beta}\)
but \(\alpha-\beta=\sqrt{(\alpha+\beta)^{2}-4 \alpha \beta}\)
\begin{aligned}
&=\frac{-\left(\sqrt{(\alpha+\beta)^{2}-4 \alpha \beta}\right)}{\alpha \beta} \\
&=\frac{-\left(\sqrt{5^{2}-4 \times 4}\right)}{4}=+\frac{3}{4}
\end{aligned}