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Properties of Conjugate of a Complex Number

If the equati...

Question

If the equations $x^{2} + 3 x + 2 = 0$ and $x^{2} + k x + 6 = 0$ have a common root then find the values of k

- 1, - 2

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5, 7

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7, - 2

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- 1, 5

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Solution

The correct option is B $5, 7$
Roots of the equation $x^{2} + 3 x + 2 = 0$ are - 2,-1

Let $x = - 2$ be common root :

$\Rightarrow 4 - 2 k + 6 = 0$

$\Rightarrow k = 5$

Let $x = - 1$ be common root

$\Rightarrow 1 - k + 6 = 0$

$\Rightarrow k = 7$

Hence $k = 5$ or $7$

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