If one root of a quadratic equation is `sqrt8` then what would definitely, be the other root?

Options

A. A) `sqrt(-8`
B. B) `2sqrt2`
C. C) `isqrt8`
D. D) none of these

Answer

To solve the problem, we need to determine the other root of a quadratic equation given that one root is \( \sqrt{8} \).

### Step-by-Step Solution:

1. **Identify the Given Root**:
We are given that one root of the quadratic equation is \( r_1 = \sqrt{8} \).

2. **Recognize the Nature of the Root**:
\( \sqrt{8} \) is an irrational number. In quadratic equations, irrational roots occur in conjugate pairs.

3. **Understand Conjugate Pairs**:
If one root is of the form \( p + \sqrt{q} \), the other root will be \( p - \sqrt{q} \). In our case, since \( \sqrt{8} \) can be expressed as \( 0 + \sqrt{8} \), the conjugate would be \( 0 - \sqrt{8} \).

4. **Calculate the Other Root**:
Therefore, the other root \( r_2 \) can be calculated as:
\[ r_2 = 0 - \sqrt{8} = -\sqrt{8} \]

5. **Final Answer**:
The other root of the quadratic equation is \( -\sqrt{8} \).

### Summary of the Solution:
If one root of a quadratic equation is \( \sqrt{8} \), the other root is definitely \( -\sqrt{8} \).