If the zeroes of the cubic polynomial f(x) = kx³-8x²+5 are alpha-beta, alpha and alpha+beta then find the value of k?

We will be using the sum of roots of a cubic polynomial to solve this.

Answer: The value of k is (8/3α) for the cubic polynomial f(x) = kx³-8x²+5

Let's solve this question step by step.

Explanation: 

Given: 

f(x) = kx³-8x²+5

Thus, a = k, b = -8, c = 0, d = 5

The zeroes or roots of the cubic polynomial are (α - β), (α), (α + β)

Now,

Sum of roots,

(α - β)+ (α)+ (α + β) = 3α ------------- (1)

Also, Sum of roots of a cubic polynomial is (-b/a)

Substitute the values

(-b/a) = -(-8/k) ------------- (2) [Since, a = k, b = -8]

Equate equation (1) and (2)

3α =  -(-8/k)

3α = (8/k)

k = 8/3α

Hence, the value of k is (8/3α) for the cubic polynomial f(x) = kx³-8x²+5.