If `alpha` and `beta` are the zeroes of the polynomial `2x^(2) - 13x + 6`, then `alpha +beta` is equal to

Options

A. `-3`
B. 3
C. `(13)/(2)`
D. `-(13)/(2)`

Answer

To find the value of \( \alpha + \beta \) for the polynomial \( 2x^2 - 13x + 6 \), we can use the relationship between the coefficients of the polynomial and its zeros.

### Step-by-Step Solution:

1. **Identify the coefficients of the polynomial**:
The given polynomial is \( 2x^2 - 13x + 6 \). Here, we can identify:
- \( A = 2 \) (coefficient of \( x^2 \))
- \( B = -13 \) (coefficient of \( x \))
- \( C = 6 \) (constant term)

2. **Use the formula for the sum of the zeros**:
The sum of the zeros \( \alpha + \beta \) of a quadratic polynomial \( Ax^2 + Bx + C \) is given by the formula:
\[ \alpha + \beta = -\frac{B}{A} \]

3. **Substitute the values of \( A \) and \( B \)**:
Substitute \( B = -13 \) and \( A = 2 \) into the formula:
\[ \alpha + \beta = -\frac{-13}{2} \]

4. **Simplify the expression**:
Simplifying the above expression gives:
\[ \alpha + \beta = \frac{13}{2} \]

5. **Final answer**:
Therefore, the value of \( \alpha + \beta \) is:
\[ \alpha + \beta = \frac{13}{2} \]