If $(x - 2)$ is one factor of $x^{2} + a x - 6 = 0$ and $x^{2} - 9 x + b = 0$ then a + b = ____

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Solution

The correct option is A 15
Since, (x -2) is one factor of $x^{2} + a x - 6 = 0$
$\Rightarrow 2^{2} + a (2) - 6 = 0$
$\Rightarrow 2 a = 2 \Rightarrow a = 1$ ...(i)
Again as (x -2) is factor of $x^{2} - 9 x + b = 0$
$\Rightarrow 2^{2} - 9 (2) + b = 0$
$\Rightarrow b = 14$ ...(ii)
Now, $a + b = 1 + 14 = 15$
Hence, Option A is correct.

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