Disproving existence of real root in some interval for a quintic equation Disprove the statement: There is a real root of equation $\frac{1}{5}x^5+\frac{2}{3}x^3+2x=0$ on the interval (1,2).
I am not sure whether to prove by counter-example or by assuming the statement is true and then proving by contradiction. 

Hint: $x$ can't be a root on the interval, as it is positive throughout, so you can divide through by $x$ and solve the resulting quadratic in $x^2$
