Hello,

The value of k is 6.

Explanation

1. Understand the Formula

For any quadratic polynomial in the standard form ax² + bx + c, the product of its zeroes (roots) is given by the formula:

Product of the zeroes = c/a

2. Identify the Coefficients

First, let's identify the values of a, b, and c from your given polynomial:

p(x) = 2x² - 3x + k

Comparing this to the standard form, we have:

• a = 2

• b = -3

• c = k

3. Set Up the Equation

The problem states that the product of the zeroes is 3.

Using the formula, we know the product of the zeroes is also c/a. So, we can set up the following equation:

c/a = 3

4. Solve for k

Now, substitute the values of 'a' and 'c' from the polynomial into the equation:

k/2 = 3

To find k, multiply both sides of the equation by 2:

k = 3 * 2

k = 6

Therefore, the value of k is 6.