Application Of Derivatives

Consider the quadratic equation $a x^2+b x+c=0$, where $2 a+3 b+6 c=0$ and let $g(x)=\frac{a x^3}{3}+\frac{b x^2}{2}+c x$

Statement I The given quadratic equation $a x^2+b x+c=0$ has atleast one root in $(0,1)$.

Statement II Rolle's theorem is applicable to $g(x){\text {on }}$ [0, 1].

Then