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  4. If x is real, then the minimum value of x2 - 8x+17 is

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Q. If $x$ is real, then the minimum value of $x^2 - 8x+17 $ is

KCETKCET 2015Complex Numbers and Quadratic Equations

Solution:

Let $y =x^{2}-8 x+17 $
$=(x-4)^{2}-16+17$
$=(x-4)^{2}+1 $
$\Rightarrow y \,\geq 1$ for all real values of x as
$(x-4)^{2} \geq \,0$
Hence , minimum value of y is 1