The common root of $x^{2} - 5 x + 6 = 0$ and $x^{2} - 8 x + 15 = 0$ is the root of $x^{2} + 4 x + q = 0$ then value of $q$ is

21

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41

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- 21

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- 41

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Solution

The correct option is C $- 21$
$x^{2} - 5 x + 6 = 0 = (x - 2) (x - 3)$
Roots are $2$ and $3$
For $x^{2} - 8 x + 15 = 0 = (x - 5) (x - 3)$
Roots are $3$ and $5$
We have common root $= 3$
We know that common root is the root of $x^{2} + 4 x + q = 0$
Putting $x = 3$ we get $9 + 12 + q = 0$
$\Rightarrow q = - 21$

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