The distance between K-axis and the axis of symmetry is 4 and one of the two roots is `-9`, then what can be the other root?

Options

A. A)9 or 19
B. B)4 or 14
C. C)1 or 17
D. D)`-5` or 13

Answer

To solve the problem, we need to find the other root (let's call it β) given that one root (α) is -9 and the distance between the K-axis and the axis of symmetry is 4.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We know one root (α) is -9.
- The distance between the K-axis and the axis of symmetry is given as 4.

2. **Using the Formula for Distance**:
- The distance between the K-axis and the axis of symmetry can be expressed as:
\[ \text{Distance} = \frac{\alpha + \beta}{2} \]
- Here, we set this equal to 4:
\[ \frac{\alpha + \beta}{2} = 4 \]

3. **Substituting the Known Root**:
- Substitute α = -9 into the equation:
\[ \frac{-9 + \beta}{2} = 4 \]

4. **Solving for β**:
- Multiply both sides by 2 to eliminate the fraction:
\[ -9 + \beta = 8 \]
- Now, add 9 to both sides to isolate β:
\[ \beta = 8 + 9 \]
\[ \beta = 17 \]

5. **Considering the Other Possibility**:
- The distance can also be considered in the negative direction, hence:
\[ \frac{-9 + \beta}{2} = -4 \]
- Multiply both sides by 2:
\[ -9 + \beta = -8 \]
- Add 9 to both sides:
\[ \beta = -8 + 9 \]
\[ \beta = 1 \]

6. **Final Answers**:
- The possible values for the other root (β) are 17 and 1.

### Summary of Results:
The other root can be either **1 or 17**.