If α, β are the zeros of the polynomial f(x) = x2 – 5x + k such that α ‒ β = 1, find the value of k.
It is given in the question that,
f (x) = x2 – 5x + k such that its coefficients are a = 1, b = - 5 and c = k
∴ 
= 
= 5 (i)
, 
= 1 (ii)
, we get:
2a = 6
a = 
= 3
Now putting the value of a in (i), we get
3 + 
= 5
= 5 – 3 = 2
= 
Hence, k = 6
15