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Nth Term of GP

If x2-ax-3=...

Question

If $x^{2} - a x - 3 = 0$ and $x^{2} + a x - 15 = 0$ have a common root, then $a =$

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Solution

The correct options are
A $2$
D $- 2$
Adding both the equations we get,
$x^{2} - 9 = 0 \Rightarrow x = \pm 3$
If $x = 3$ ,
$\Rightarrow 9 - 3 a - 3 = 0 \Rightarrow a = 2$ and
$9 + 3 a - 15 = 0 \Rightarrow a = 2$
If $x = - 3, \Rightarrow 9 + 3 a - 3 = 0 \Rightarrow a = - 2$
and $9 - 3 a - 15 = 0 \Rightarrow a = - 2$

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