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.
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)
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