Multiple choice

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

  1. $At\quad least\quad one\quad root\quad in\quad [0,1]$
  2. $At\quad least\quad one\quad root\quad in\quad [\cfrac{-1}{2},\cfrac{1}{2}]$
  3. $At\quad least\quad one\quad root\quad in\quad [-1,0]$
  4. $At\quad least\quad two\quad root\quad in\quad [0,2]$
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D Correct answer

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