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Let $a, b, c \in R$ such that no two of them are equal and satisfy $|\begin{matrix} 2 a & b & c \\ b & c & 2 a \\ c & 2 a & b \end{matrix}| = 0$ then equation $24 a x^{2} + 4 b x + c = 0$ has

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Atleast one root in $[0, 1]$

Atleast one root in $[\frac{- 1}{2}, \frac{1}{2}]$

Atleast one root in $[- 1, 0]$

Atleast one root in $[0, 2]$

answer is A.

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