The sum of zeroes of quadratic polynomial is `-sqrt2` and product is 7, that quadratic polynomial is :

Options

A. `x^(2)-sqrt2x+7`
B. `x^(2)+sqrt2x+7`
C. `x^(2)-sqrt2x-7`
D. `x^(2)+sqrt2x-7`

Explanation

To find the quadratic polynomial given the sum and product of its zeroes, we can follow these steps:

### Step 1: Identify the sum and product of the zeroes
Given:
- Sum of the zeroes (α + β) = -√2
- Product of the zeroes (αβ) = 7

### Step 2: Write the general form of the quadratic polynomial
The standard form of a quadratic polynomial based on its zeroes is given by:
\[ p(x) = x^2 - (α + β)x + (αβ) \]

### Step 3: Substitute the values of the sum and product into the polynomial
Substituting the known values into the polynomial:
\[ p(x) = x^2 - (-√2)x + 7 \]

### Step 4: Simplify the polynomial
This simplifies to:
\[ p(x) = x^2 + √2x + 7 \]

### Final Result
Thus, the quadratic polynomial is:
\[ p(x) = x^2 + √2x + 7 \]

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