Zeroes of a Polynomial:
The zeroes of a polynomial are the values of the variable for which the polynomial becomes zero. In other words, they are the values of 'x' that satisfy the equation P(x) = 0, where P(x) is the given polynomial.

Given Polynomial:
The given polynomial is 3x^2 - 3.

Finding the Zeroes:
To find the zeroes of the polynomial, we need to set the polynomial equal to zero and solve for 'x'.

3x^2 - 3 = 0

Adding 3 to both sides of the equation, we get:

3x^2 = 3

Dividing by 3 on both sides, we obtain:

x^2 = 1

Taking the square root of both sides, we have:

x = ±1

Therefore, the zeroes of the polynomial 3x^2 - 3 are x = 1 and x = -1.

Relationship between Zeroes and Coefficients:
The relationship between the zeroes of a polynomial and its coefficients is described by Vieta's formulas. Vieta's formulas state that the sum of the zeroes of a quadratic polynomial is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term, and the product of the zeroes is equal to the constant term divided by the coefficient of the quadratic term.

In the given polynomial 3x^2 - 3, the coefficient of the linear term is 0 and the coefficient of the quadratic term is 3. Therefore, according to Vieta's formulas:

- The sum of the zeroes is (-0)/3 = 0/3 = 0.
- The product of the zeroes is (-3)/3 = -1.

Hence, the zeroes of the polynomial 3x^2 - 3 satisfy the relationship described by Vieta's formulas.