Roots of Cubic Polynomial

Let the roots of $5x^3 + cx^2 - 10x + 9 = 0$ be $r, -r, k$. Sum of roots: $r + (-r) + k = -\frac{c}{5} \implies k = -\frac{c}{5}$. Sum of product of roots taken two at a time: $r(-r) + r k + (-r)k = -\frac{10}{5} = -2 \implies -r^2 = -2 \implies r^2 = 2$. Product of roots: $r(-r)k = -\frac{9}{5} \implies -r^2 k = -\frac{9}{5} \implies -2k = -\frac{9}{5} \implies k = \frac{9}{10}$. Since $k = -\frac{c}{5}$, we have $-\frac{c}{5} = \frac{9}{10} \implies c = -\frac{45}{10} = -\frac{9}{2}$.