If the roots of the equation x³ − 12x² + 39x − 28 = 0 are in A.P., then their common difference is:

Correct option is C

Given:

Concept:
For cubic ax³ + bx² + cx + d = 0,
Sum of roots = −b/a
Sum of product of roots two at a time = c/a
Product of roots = −d/a

Solution:

From sum of roots:
(a − d) + a + (a + d) = 3a = 12
=> a = 4

From product of roots:
(a − d)a(a + d) = 28
=> a(a² − d²) = 28
=> 4(16 − d²) = 28
=> 64 − 4d² = 28
=> 4d² = 36
=> d² = 9
=> d = ±3