> Let $a,b,c \in \mathbb R$ such that no two of them are equal and
> satisfy $\det\begin{bmatrix}2a&b&c\\b&c&2a\\c&2a&b\end{bmatrix} = 0$,
> then the equation $24ax^2 + 4bx +c=0$ has:
>
> a) atleast one root in $[0,\frac 12]$
>
> b) at least one root in $[-\frac 12, 0)$
>
> c) at least one root in $[1,2]$
>
> d) none of these
> satisfy $\det\begin{bmatrix}2a&b&c\\b&c&2a\\c&2a&b\end{bmatrix} = 0$,
> then the equation $24ax^2 + 4bx +c=0$ has:
>
> a) atleast one root in $[0,\frac 12]$
>
> b) at least one root in $[-\frac 12, 0)$
>
> c) at least one root in $[1,2]$
>
> d) none of these