Which of the following is equivalent to

[tex]-b - \sqrt{b^2 - 4ac}[/tex]

when [tex]a = 4[/tex], [tex]b = -5[/tex], and [tex]c = 1[/tex]?

A. -4
B. 2
C. 3
D. 4



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