For the given polynomial p(x) = `2x^(2) - 8x + 6`, what is the sum of its zeroes is.

Options

A. -1
B. `(1)/(3)`
C. 4
D. 3

Answer

To find the sum of the zeroes of the polynomial \( p(x) = 2x^2 - 8x + 6 \), we can use the formula for the sum of the roots of a quadratic polynomial. The general form of a quadratic polynomial is given by:

\[ p(x) = Ax^2 + Bx + C \]

where:
- \( A \) is the coefficient of \( x^2 \),
- \( B \) is the coefficient of \( x \), and
- \( C \) is the constant term.

### Step 1: Identify the coefficients
From the polynomial \( p(x) = 2x^2 - 8x + 6 \), we can identify:
- \( A = 2 \)
- \( B = -8 \)
- \( C = 6 \)

### Step 2: Use the formula for the sum of the zeroes
The sum of the zeroes (roots) of the polynomial, denoted as \( \alpha + \beta \), can be calculated using the formula:

\[ \text{Sum of the zeroes} = -\frac{B}{A} \]

### Step 3: Substitute the values of \( A \) and \( B \)
Now, substituting the values of \( A \) and \( B \) into the formula:

\[ \text{Sum of the zeroes} = -\frac{-8}{2} \]

### Step 4: Simplify the expression
Now, simplify the expression:

\[ \text{Sum of the zeroes} = \frac{8}{2} = 4 \]

### Conclusion
Thus, the sum of the zeroes of the polynomial \( p(x) = 2x^2 - 8x + 6 \) is \( 4 \).

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