What is the sum of the the roots of the equation 4x^3 + 5x^2 - 8x = 0 ? Express your answer as a decimal to the nearest hundredth.
We can factor the equation as 4x(x2+45x−2)=0. The first factor, 4x, never equals 0, so the only way the equation is true is if x2+45x−2=0. By the quadratic formula, the roots of this equation are
[x = \frac{-5 \pm \sqrt{25 + 16}}{2} = -\frac{5 \pm 7}{2}.]The sum of the roots is then 2−5−5+7+7 = 1.0.
