Find a quadratic polynomial, the sum and product of whose zeros is 4 and 1 respectively.

Answer

To find a quadratic polynomial given the sum and product of its zeros, we can use the standard form of a quadratic polynomial, which is:

\[ P(x) = x^2 - (sum \ of \ zeros) \cdot x + (product \ of \ zeros) \]

Given:
- Sum of the zeros (\( \alpha + \beta \)) = 4
- Product of the zeros (\( \alpha \cdot \beta \)) = 1

### Step 1: Write the polynomial using the sum and product of zeros

Using the formula mentioned above, we can substitute the values of the sum and product of the zeros:

\[ P(x) = x^2 - (4) \cdot x + (1) \]

### Step 2: Simplify the polynomial

Now we simplify the expression:

\[ P(x) = x^2 - 4x + 1 \]

### Final Answer

Thus, the quadratic polynomial is:

\[ P(x) = x^2 - 4x + 1 \]

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