Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
`0,sqrt(5)`

Answer

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

### Step 1: Identify the sum and product of the zeroes
We are given:
- Sum of the zeroes (α + β) = 0
- Product of the zeroes (α * β) = √5

### Step 2: Use the standard form of a quadratic polynomial
The standard form of a quadratic polynomial based on the sum and product of its zeroes is given by:
\[ P(x) = x^2 - (sum \ of \ zeroes) \cdot x + (product \ of \ zeroes) \]

### Step 3: Substitute the values into the polynomial
Substituting the values we have:
- Sum of zeroes = 0
- Product of zeroes = √5

So, we can write:
\[ P(x) = x^2 - (0) \cdot x + \sqrt{5} \]

### Step 4: Simplify the polynomial
Since multiplying by zero does not change the value, we simplify it to:
\[ P(x) = x^2 + \sqrt{5} \]

### Final Answer
Thus, the required quadratic polynomial is:
\[ P(x) = x^2 + \sqrt{5} \]

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