(C) The given expression is ${x^2} - 8x + 17$.We can rewrite this by completing the square:${x^2} - 8x + 17 = {x^2} - 8x + 16 + 1 = {(x - 4)^2} + 1$.S

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(C) The given expression is ${x^2} - 8x + 17$.We can rewrite this by completing the square:${x^2} - 8x + 17 = {x^2} - 8x + 16 + 1 = {(x - 4)^2} + 1$.Since $x$ is a real number,the square of any real number is always non-negative,i.e.,${(x - 4)^2} \ge 0$.The minimum value of ${(x - 4)^2}$ is $0$ when $x = 4$.Therefore,the minimum value of the expression is $0 + 1 = 1$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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

A
$-1$
B
$0$
C
$1$
D
$2$

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4-2.Quadratic Equations and Inequations

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Solution of quadratic equations and Nature of roots

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

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