If $x^{2} + k x + 6 = (x + 2) (x + 3)$ for all $x$ , the value of $k$ is

1

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5

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3

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Solution

The correct option is B $5$
Given: $x^{2} + k x + 6 = (x + 2) (x + 3)$ for all values of $x$
To find the value of $k$
Sol: $x^{2} + k x + 6 = (x + 2) (x + 3) ⟹ x^{2} + k x + 6 = x (x + 3) + 2 (x + 3) ⟹ x^{2} + k x + 6 = x^{2} + 3 x + 2 x + 6 ⟹ x^{2} + k x + 6 = x^{2} + 5 x + 6$
Equating both sides in the above condition we get,
The value of $k = 5$

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