Given: α and β are zeroes of f(x) = x2 ‒ 5x + k
and α – β = 1
We know that,
α + β = Sum of zeros = -(coefficient of x)/(coefficient of x2) = 5
α β = Product of zeros = (constant term)/(coefficient of x2) = k
Now solving α – β = 1 and α + β = 5, we get:
α = 3 and β = 2
Again: α β = k (putting value of α and β)
k = 6.