**Quadratic Polynomials**

A quadratic polynomial is a polynomial of degree 2. It can be represented in the form:

f(x) = ax^2 + bx + c

where a, b, and c are constants.

**Sum and Product of Zeros**

The zeros of a quadratic polynomial are the values of x that make the polynomial equal to zero. Let's assume the zeros of the quadratic polynomial are p and q.

According to the problem, the sum of the zeros is 3 and the product of the zeros is 2. Mathematically, this can be represented as:

p + q = 3
p * q = 2

**Finding the Quadratic Polynomial**

To find the quadratic polynomial, we need to determine the values of a, b, and c in the general form of the polynomial.

We know that the sum of the zeros is equal to the negative coefficient of the linear term (b) divided by the coefficient of the quadratic term (a). Therefore, we have:

p + q = -b/a

From the equation p + q = 3, we can deduce that -b/a = 3.

Similarly, we know that the product of the zeros is equal to the constant term (c) divided by the coefficient of the quadratic term (a). Therefore, we have:

p * q = c/a

From the equation p * q = 2, we can deduce that c/a = 2.

**Solving for a, b, and c**

To solve for a, b, and c, we can set up a system of equations using the given information:

-b/a = 3
c/a = 2

By cross-multiplying, we can rewrite these equations as:

-b = 3a
c = 2a

Now, we can substitute the value of c from the second equation into the first equation:

-2a = 3a

Simplifying, we get:

5a = 0

This implies that a = 0.

Substituting the value of a into the equations for b and c, we get:

-b = 3(0)
c = 2(0)

Simplifying further, we find that b = 0 and c = 0.

**The Quadratic Polynomial**

Now that we have determined the values of a, b, and c, we can write the quadratic polynomial:

f(x) = ax^2 + bx + c = 0x^2 + 0x + 0 = 0

Therefore, the quadratic polynomial with sum of zeros as 3 and product of zeros as 2 is f(x) = 0.