The quadratic polynomial, the sum, and the product of whose zeroes are 3 and −2 respectively, is

The quadratic polynomial can be found using the sum and product of its roots. The general form of a quadratic polynomial is ax^2 + bx + c.

Given that the sum of the roots (α + β) is 3 and the product of the roots (αβ) is -2, we can use the relationships:

• The sum of the roots is equal to -b/a. So, -b/a = 3.
• The product of the roots is equal to c/a. So, c/a = -2.

Assuming that the coefficient of x^2 (a) is 1 (this is usually the case unless stated otherwise), we can rewrite the quadratic polynomial as:

x^2 - (sum of roots)x + product of roots = x^2 - 3x - 2

So, the quadratic polynomial whose sum and product of zeroes are 3 and -2 respectively is x^2 - 3x - 2.