Let α , β and γ be the roots of the equation x 3 + 6 x 2 - p x - 42 = 0 . If α , β and γ are in arithmetic progression then α + β + γ =

Question

Let α , β and γ be the roots of the equation x 3 + 6 x 2 - p x - 42 = 0 . If α , β and γ are in arithmetic progression then α + β + γ =, 10, 11, 12, 13

MARKS App · Accepted Answer

Let, α = β - d and γ = β + d β - d , β , β + d are the roots β - d + β + β + d = - 6 ⇒ β = - 2 β - d β β + d = 42 ⇒ - 2 - d - 2 - 2 + d = 4 2 ⇒ 2 + d 2 2 - d = - 42 ⇒ 4 - d 2 = - 2 1 ⇒ d 2 = 25 ⇒ d = ± 5 ⇒ The roots are - 7 , - 2,3 ⇒ α + β + γ = 1 2

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