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Let a ,b , c in R such that no two of t...

Let `a ,b , c in R` such that no two of them are equal and satisfy `|2a b c b c2a c2a b|=0,` then equation `24 a x^2+4b x+c=0` has at last one root in `[0,1]` at last one root in `[-1/2,1/2]` at last one root in `[-1,0]` at last two roots in `[0,2]`

A

atleast one root in `[0,(1)/(2)]`

B

atleast one root in `[-(1)/(2),(1)/(2)]`

C

atleast one root in `[-1,0]`

D

atleast one root in [0,2]

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The correct Answer is:
A
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