If α and β are the roots of the equation x 2 + x + c = 0 such that α + β , α 2 + β 2 and α 3 + β 3 are in arithmetic progression, then c is equal to

Step-by-step solution

Given, α + β = - 1 , α β = c Also, 2 a 2 + β 2 = α + β + α 3 + β 3 ⇒ 2 α + β 2 - 2 α β = α + β + α + β 3 - 3 α β α + β ⇒ 2 - 4 c = - 2 + 3 c ⇒ c = 4 7