If $x^{2} + 4 a x + 3 = 0$ and $2 x^{2} + 3 a x - 9 = 0$ have a common root, then the value of 'a' is ______.

\pm 3

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\pm 1

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Only 1

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\pm 2

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Solution

The correct option is A $\pm 3$
Let the common root of the equations be $p$ .
Then, $p^{2} + 4 a p + 3 = 0$ $\Rightarrow$ $2 p^{2} + 8 a p + 6 = 0$
and $2 p^{2} + 3 a p - 9 = 0$
Equating both the equations
$2 p^{2} + 8 a p + 6$ $=$ $2 p^{2} + 3 a p - 9$
$\Rightarrow$ $5 a p = - 15$
$\Rightarrow$ $a p = - 3$
Substitute the value of $a p$ in the first equation
Then, $p^{2} + 4 (- 3) + 3 = 0$
$\Rightarrow$ $p^{2} = 9$
$\Rightarrow$ $p = \pm 3$
$\Rightarrow$ $a = \pm 1$
$∴$ Option B is correct.

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