If the sum of the zeroes of the polynomial (kx² − 3x − 6k) is equal to their…

To find the value of k for the polynomial kx² - 3x - 6k, we use the relationship between the coefficients of a quadratic polynomial and its zeroes.

Step-by-Step Solution
Identify coefficients: For a quadratic polynomial in the form ax² + bx + c:

a = k

b = -3

c = -6k

Define Sum and Product of Zeroes:

The sum of zeroes = -b / a = -(-3) / k = 3 / k

The product of zeroes = c / a = -6k / k = -6

Set up the equation: The problem states that the sum of the zeroes is equal to their product:
Sum of zeroes = Product of zeroes
3 / k = -6

Solve for k:

Multiply both sides by k: 3 = -6k

Divide by -6: k = 3 / -6

k = -1/2