If the roots are same, then the. roots must be

Options

A. negative
B. rational
C. irrational
D. complex conjugate

Answer

To solve the question "If the roots are same, then the roots must be", we will analyze the conditions under which a quadratic equation has equal roots.

### Step-by-Step Solution:

1. **Understanding the Quadratic Equation**:
A quadratic equation is generally expressed in the form \( ax^2 + bx + c = 0 \).

2. **Roots of the Quadratic Equation**:
The roots of the quadratic equation can be found using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

3. **Condition for Equal Roots**:
For the roots to be the same (or equal), the discriminant must be zero. The discriminant \( D \) is given by:
\[ D = b^2 - 4ac \]
Therefore, for equal roots:
\[ b^2 - 4ac = 0 \]

4. **Finding the Roots**:
If \( D = 0 \), substituting this back into the quadratic formula gives:
\[ x = \frac{-b \pm 0}{2a} = \frac{-b}{2a} \]
This means that the roots are both equal to \( \frac{-b}{2a} \).

5. **Conclusion**:
Since the roots are the same, we can conclude that the roots must be:
\[ x = \frac{-b}{2a} \]

### Final Answer:
If the roots are the same, then the roots must be \( \frac{-b}{2a} \).

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