Question

If the roots of the equation x³ -  12x² + 39x - 28 = 0 are in AP, then their common difference will be

(A)  ± 1

(B)  ± 2 

(C)  ± 3 

(D)  ± 4

Answer 1

Correct option  (C) ± 3

Let roots be a − d, a, a + d which are in AP. The common difference is d.

x³ - 12x² + 39x - 28 = 0

Adding the three roots we have

a - d + a + a + d = 12

⇒ 3a = 12 ⇒ a = 4

Product of the three roots is

a(a² - d²) = 28 ⇒ d² = 9 ⇒ d = ±3