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The quadratic equation $3 {ax}^{2} + 2 bx + c = 0$ has atleast one root between 0 and 1, if

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a + b = c

a + b + c = 0

3a + 2b + c = 0

c = 0

answer is A.

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Detailed Solution

$f (x) = {ax}^{2} + {bx}^{2} + cx f (0) = 0, f (1) = a + b + c$

$∴ x \in (0, 1)$ at least one root

$\Rightarrow f (0) = f (1) \Rightarrow a + b + c = 0$

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