If one of the zeroes 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 zero is \( -1 \), we can follow these steps:

### Step 1: Identify the coefficients of the polynomial
The polynomial is in the standard form \( ax^2 + bx + c \), where:
- \( a = 1 \)
- \( b = -7 \)
- \( c = -8 \)

### Step 2: Use the relationship between the roots
For a quadratic polynomial \( ax^2 + bx + c = 0 \), if the roots are \( \alpha \) and \( \beta \), then:
- \( \alpha + \beta = -\frac{b}{a} \)
- \( \alpha \beta = \frac{c}{a} \)

### Step 3: Substitute the known zero into the equation
Let \( \alpha = -1 \) (the known zero) and \( \beta = A \) (the other zero we need to find). According to the sum of the roots:
\[ -1 + A = -\frac{-7}{1} \]
This simplifies to:
\[ -1 + A = 7 \]

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

### Conclusion
Thus, the other zero of the polynomial \( f(x) = x^2 - 7x - 8 \) is \( 8 \).

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