For what positive value of $m$ , the equation ${12 x}^{2} + 4 (m + 1) x + 3 = 0$ will have equal roots?

1

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4

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3

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2

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Solution

The correct option is B $2$
Given equation is:
${12 x}^{2} + 4 (m + 1) x + 3 = 0$
For equal roots, we have
$D = 0$
$\Rightarrow b^{2} - 4 a c = 0$
${4 (m + 1)}^{2} - 4 (12) (3) = 0$
${16 (m + 1)}^{2} - 144 = 0$
$\Rightarrow (m + 1)^{2} = 9$
$m + 1 = 3$
$∴ m = 2$

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