If α and β are the roots of the equation x 2 - 2 x + 3 = 0 , then the sum of roots of the equation having roots as α 3 - 3 α 2 + 5 α - 2 and β 3 - β 2 + β + 5 is

Step-by-step solution

Since, α 2 - 2 α + 3 = 0 ⇒ α 3 - 3 α 2 + 5 α - 2 = α α 2 - 2 α + 3 - α 2 - 2 α + 3 + 1 = 1 And β 2 - 2 β + 3 = 0 ⇒ β 3 - β 2 + β + 5 = β β 2 - 2 β + 3 + β 2 - 2 β + 3 + 2 = 2 So, the required equation is x 2 - 2 + 1 x + 2.1 = 0 ⇒ x 2 - 3 x + 2 = 0 Sum of roots = 3