For what value of 'm', the equation $(3 m + 1) x^{2} + 2 (m + 1) x + m = 0$ have equal root?

1, - 1 / 2

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2

4

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4

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3

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Solution

The correct option is A $1, - 1 / 2$
For equal roots $D = b^{2} - 4 a c = 0$
$\Rightarrow [2 (m + 1)]^{2} - 4 m (3 m + 1) = 0$
$\Rightarrow m^{2} + 2 m + 1 - 3 m^{2} - m = 0$
$\Rightarrow - 2 m^{2} + m + 1 = 0$
$\Rightarrow 2 m^{2} - m - 1 = 0 \Rightarrow (m - 1) (m + \frac{1}{2}) = 0$
$\Rightarrow m = 1, \frac{- 1}{2}$

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