jmc

First we can factor out an $x$. That gives us the equation $x(4x^2+5x-8)=0$. This product is equal to zero when $x=0$ or when $(4x^2+5x-8)=0$. This root of zero contributes nothing to the sum of the roots. Now we don't actually need to factor $4x^2+5x-8=0$ into the product of two binomials to find the sum of the roots. (It doesn't factor nicely.) If we divide both sides of this equation by 4, we get $x^2+(5/4)x-2=0$. The coefficient of the middle term (5/4) is the opposite of the sum of the roots, so our answer is $\boxed{-1.25}$.