To solve the expression [tex]\(-b - \sqrt{b^2 - 4ac}\)[/tex] given [tex]\(a = 4\)[/tex], [tex]\(b = -5\)[/tex], and [tex]\(c = 1\)[/tex], follow these steps:
1. Substitute the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] into the expression:
[tex]\[
-b - \sqrt{b^2 - 4ac} \quad \text{where} \quad a = 4, \quad b = -5, \quad c = 1
\][/tex]
2. Evaluate [tex]\(-b\)[/tex]:
[tex]\[
-(-5) = 5
\][/tex]
3. Calculate [tex]\(b^2\)[/tex]:
[tex]\[
(-5)^2 = 25
\][/tex]
4. Calculate [tex]\(4ac\)[/tex]:
[tex]\[
4 \times 4 \times 1 = 16
\][/tex]
5. Subtract [tex]\(4ac\)[/tex] from [tex]\(b^2\)[/tex]:
[tex]\[
25 - 16 = 9
\][/tex]
6. Calculate the square root of the result:
[tex]\[
\sqrt{9} = 3
\][/tex]
7. Combine the results:
[tex]\[
5 - 3 = 2
\][/tex]
Therefore, the expression [tex]\(-b - \sqrt{b^2 - 4ac}\)[/tex] evaluates to 2 when [tex]\(a = 4\)[/tex], [tex]\(b = -5\)[/tex], and [tex]\(c = 1\)[/tex].
Hence, the correct option is:
B) 2
