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