The equation $(m + 1) x^{2} + 2 m x + 5 x + m + 3 = 0$ has equal roots Find the value of m

-11/4

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-13/4

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-15/4

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-17/4

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Solution

The correct option is B -13/4
For an equation $a x^{2} + b x + c = 0$ , to have equal roots, the discriminant $△ = b^{2} - 4 a c$ should be $= 0$
For the given equation,
$b^{2} - 4 a c = 0$
$=> {(2 m + 5)}^{2} - 4 \times (m + 1) \times (m + 3) = 0$
$=> 4 m^{2} + 25 + 20 m - 4 \times [m^{2} + 3 + 4 m] = 0$
$=> 4 m^{2} + 25 + 20 m - 4 m^{2} - 12 - 16 m = 0$
$=> 4 m + 13 = 0$
$=> m = - \frac{13}{4}$

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