Existence of a Solution in the Open Interval (0, 1) for a Cubic Equation with Real Coefficients
Let $a,b,c\in \mathbb{R}$. Show that there exists $x\in (0,1)$ such that
$$4ax^3+3bx^2+2cx=a+b+c.$$
Show Hint:Let $a,b,c\in \mathbb{R}$. Show that there exists $x\in (0,1)$ such that
$$4ax^3+3bx^2+2cx=a+b+c.$$
Show Hint: