The minimum value of the expression $f (x) = x^{2} + 4 x + 17$ for real value of $x$ is

17

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13

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12

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21

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Solution

The correct option is B $13$
The Minimum value of the expression $f (x) = x^{2} + 4 x + 17$ is

$\frac{4 a c - b^{2}}{4 a} = \frac{4 (1) (17) - (4)^{2}}{4 (1)} = \frac{68 - 16}{4} = \frac{52}{4} = 13$

Option B is correct.

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