If $(m^{2} - 3) x^{2} + 3 m x + 3 m + 1 = 0$ has roots which are reciprocals of each other, then the value of $m$ equals to

4

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1

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2

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None of these

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Solution

The correct option is A $4$
If the roots are reciprocal then the product of the roots of the equation equal to $1$
$(m^{2} - 3) x^{2} + 3 m x + 3 x + 1 = 0$
Product of the roots $= \frac{c}{a}$
$\frac{3 m + 1}{m^{2} - 3} = 1$
Or $m^{2} - 3 m - 4 = 0$
Or $m^{2} - 4 m + m - 4 = 0$
Or $(m + 1) (m - 4) = 0$
$m = 4$ or $m = - 1$
$∴$ Answer is $4$

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