Find a quadratic polynomial with 0 , `sqrt5` as the sum and product of its zeros respectively.

Answer

To find a quadratic polynomial with the sum of its zeros as 0 and the product of its zeros as \(\sqrt{5}\), we can follow these steps:

### Step 1: Define the zeros
Let the zeros of the quadratic polynomial be \(\alpha\) and \(\beta\). According to the problem, we have:
- Sum of the zeros: \(\alpha + \beta = 0\)
- Product of the zeros: \(\alpha \beta = \sqrt{5}\)

### Step 2: Use the standard form of a quadratic polynomial
The standard form of a quadratic polynomial with zeros \(\alpha\) and \(\beta\) can be expressed as:
\[ f(x) = x^2 - (\alpha + \beta)x + \alpha \beta \]

### Step 3: Substitute the values of sum and product
Substituting the values we have:
- \(\alpha + \beta = 0\)
- \(\alpha \beta = \sqrt{5}\)

Thus, the polynomial becomes:
\[ f(x) = x^2 - (0)x + \sqrt{5} \]

### Step 4: Simplify the polynomial
This simplifies to:
\[ f(x) = x^2 + \sqrt{5} \]

### Final Answer
The required quadratic polynomial is:
\[ f(x) = x^2 + \sqrt{5} \]

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