Answer :
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
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