If one of the zero of the polynomial `f (x) = x ^(2) - 7x - 8` is -1, then find the other zero .

Options

A. 7
B. 1
C. 8
D. 5

Answer

To find the other zero of the polynomial \( f(x) = x^2 - 7x - 8 \) given that one of the zeros is -1, we can follow these steps:

### Step 1: Identify the given polynomial and the known zero
The polynomial is:
\[ f(x) = x^2 - 7x - 8 \]
We know that one of the zeros (roots) is:
\[ \alpha = -1 \]

### Step 2: Use the relationship between the roots
For a quadratic polynomial \( ax^2 + bx + c = 0 \), the sum of the roots \( \alpha + \beta \) can be found using the formula:
\[ \alpha + \beta = -\frac{b}{a} \]
In our polynomial, \( a = 1 \) and \( b = -7 \). Thus, we have:
\[ \alpha + \beta = -\frac{-7}{1} = 7 \]

### Step 3: Substitute the known root into the sum of roots equation
We already know that one root \( \alpha = -1 \). We can substitute this into the sum of roots equation:
\[ -1 + \beta = 7 \]

### Step 4: Solve for the other root
To find \( \beta \), we can rearrange the equation:
\[ \beta = 7 + 1 = 8 \]

### Conclusion
Thus, the other zero of the polynomial is:
\[ \beta = 8 \]