Let $ax^2+bx+c=0$ be a quadratic equation, where $a,b,c\in\mathbb{R}$. If $2a+3b+6c=0$, then show that this equation will have atleast one root in $(0,1)$.
I think it involves either Rolle's Theorem or Lagrange's Mean Value Theorem, but can't think further. Please help, and yes, thanks in advance!
Best Answer
Hint: Another way, beside's to @Berci's comment is to consider the function $$f(x)=\frac{1}{3}ax^3+\frac{1}{2}bx^2+cx$$ on $I=(0,1)$.