If α, β and γ are the zeroes of $2x^3+x^2-5x+2$, the value of 1/α + 1/β + 1/γ is:

Put the fractions over a common denominator: $\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }=\frac{\alpha \beta +\beta \gamma +\gamma \alpha }{\alpha \beta \gamma }$. Here $\alpha \beta +\beta \gamma +\gamma \alpha =\frac{c}{a}=-\frac{5}{2}$ and $\alpha \beta \gamma =-\frac{d}{a}=-\frac{2}{2}=-1$, so the value is $\frac{-5/2}{-1}=\frac{5}{2}.-\frac{5}{2}$ misses the minus sign in $-\frac{d}{a}$; $\frac{1}{2}$ puts the sum $\alpha +\beta +\gamma =-\frac{1}{2}$ on top instead of the pairwise sum; $\frac{2}{5}$ turns the fraction upside down.