To find the value of the expression [tex]\(\left|a^2 - 2ac + 5b\right|\)[/tex] when [tex]\(a = 8\)[/tex], [tex]\(b = 3\)[/tex], and [tex]\(c = 6\)[/tex], we follow these steps:
1. Substitute the given values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] into the expression [tex]\(a^2 - 2ac + 5b\)[/tex].
[tex]\[
a = 8, \quad b = 3, \quad c = 6
\][/tex]
2. Calculate [tex]\(a^2\)[/tex]:
[tex]\[
a^2 = 8^2 = 64
\][/tex]
3. Calculate [tex]\(-2ac\)[/tex]:
[tex]\[
-2ac = -2 \cdot 8 \cdot 6 = -96
\][/tex]
4. Calculate [tex]\(5b\)[/tex]:
[tex]\[
5b = 5 \cdot 3 = 15
\][/tex]
5. Sum these results to find the value inside the absolute value:
[tex]\[
a^2 - 2ac + 5b = 64 - 96 + 15
\][/tex]
6. Perform the arithmetic operations step-by-step:
[tex]\[
64 - 96 = -32
\][/tex]
[tex]\[
-32 + 15 = -17
\][/tex]
So, the expression inside the absolute value is [tex]\(-17\)[/tex].
7. Apply the absolute value:
[tex]\[
\left| -17 \right| = 17
\][/tex]
Therefore, the value of the expression [tex]\(\left|a^2 - 2ac + 5b\right|\)[/tex] is:
[tex]\[
\boxed{17}
\][/tex]
So, the correct answer is:
C. 17
