If α and β are the zeroes of $5x^2-8x-3$, the value of α²β² is:

${\alpha }^2{\beta }^2=(\alpha \beta {)}^2$, and $\alpha \beta =\frac{c}{a}=-\frac{3}{5}$, so the value is ${\left(-\frac{3}{5}\right)}^2=\frac{9}{25}$. A square is never negative, which rules out $-\frac{9}{25}$ at a glance. $\frac{3}{5}$ forgets to square (and drops the sign); $\frac{64}{25}$ squares the sum $\frac{8}{5}$ instead of the product.