**Quadratic Polynomial with Given Zeros**

To find the quadratic polynomial with the given zeros, we can use the concept of Vieta's formulas. Vieta's formulas state that the sum and product of the roots of a quadratic polynomial can be related to its coefficients.

Let's start by finding the sum and product of the given zeros.

Given zeros:
α = 1 - a / 1 - a
β = 1 - b
We are also given the quadratic polynomial:
f(x) = 3x^2 + 2x + 1

**Finding the Sum of Zeros**

The sum of the zeros of a quadratic polynomial is given by the formula:
Sum of zeros = - (coefficient of x) / (coefficient of x^2)

In this case, the coefficient of x^2 is 3 and the coefficient of x is 2. Therefore,
Sum of zeros = -2/3

**Finding the Product of Zeros**

The product of the zeros of a quadratic polynomial is given by the formula:
Product of zeros = constant term / (coefficient of x^2)

In this case, the constant term is 1 and the coefficient of x^2 is 3. Therefore,
Product of zeros = 1/3

**Using Vieta's Formulas**

Now that we have the sum and product of the zeros, we can use Vieta's formulas to find the quadratic polynomial.

Vieta's formulas state that for a quadratic polynomial ax^2 + bx + c, the sum of the zeros is equal to -b/a and the product of the zeros is equal to c/a.

Let's substitute the values we found into Vieta's formulas:

-2/3 = -b/3 (sum of zeros)
b = 2

1/3 = 1/3c (product of zeros)
c = 1

Therefore, the quadratic polynomial with the given zeros is:
f(x) = 3x^2 + 2x + 1

**Explanation**

In this problem, we are given the zeros of a quadratic polynomial and we need to find the quadratic polynomial using Vieta's formulas. Vieta's formulas help us relate the coefficients of a quadratic polynomial to its zeros. By finding the sum and product of the zeros, we can substitute these values into Vieta's formulas to determine the coefficients of the quadratic polynomial. In this case, we found that the quadratic polynomial with the given zeros is f(x) = 3x^2 + 2x + 1.