If `f(x)=x^2-px+q` is a quadratic polynomial then, the sum of zeroes of the quadratic polynomial is:

Options

A. `-p`
B. p
C. q
D. `-q`

Answer

To find the sum of the zeroes of the quadratic polynomial \( f(x) = x^2 - px + q \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the General Form of a Quadratic Polynomial**:
The general form of a quadratic polynomial is given by:
\[ f(x) = ax^2 + bx + c \]
where \( a \), \( b \), and \( c \) are constants.

2. **Compare with the Given Polynomial**:
In our case, the polynomial is:
\[ f(x) = x^2 - px + q \]
By comparing, we can identify:
- \( a = 1 \)
- \( b = -p \)
- \( c = q \)

3. **Use the Formula for the Sum of Zeroes**:
The sum of the zeroes (roots) of a quadratic polynomial is given by the formula:
\[ \alpha + \beta = -\frac{b}{a} \]
where \( \alpha \) and \( \beta \) are the zeroes of the polynomial.

4. **Substitute the Values of \( a \) and \( b \)**:
Now we substitute the values of \( a \) and \( b \) into the formula:
\[ \alpha + \beta = -\frac{-p}{1} \]

5. **Simplify the Expression**:
Simplifying the right-hand side gives:
\[ \alpha + \beta = \frac{p}{1} = p \]

6. **Conclusion**:
Therefore, the sum of the zeroes of the quadratic polynomial \( f(x) = x^2 - px + q \) is:
\[ \alpha + \beta = p \]

### Final Answer:
The sum of the zeroes of the quadratic polynomial is \( p \).

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