Let α , β be the roots of the equation x 2 - 2 x + 6 = 0 and 1 α 2 + 1 , 1 β 2 + 1 be the roots of the equation x 2 + a x + b = 0 . Then the roots of the equation x 2 - a + b - 2 x + a + b + 2 = 0 are :

Step-by-step solution

Given α , β be the roots of the equation x 2 - 2 x + 6 = 0 So sum of roots will be α + β = 2 and product of roots will be α β = 6 And also given 1 α 2 + 1 and 1 β 2 + 1 are roots of x 2 + a x + b = 0 So sum of roots will be - a = 1 α 2 + 1 + 1 β 2 + 1 ⇒ a = - 1 α 2 - 1 β 2 - 2   . . . . . 1 And similarly product of roots will be, b = 1 α 2 + 1 β 2 + 1 + 1 α 2 β 2   . . . . 2 Now adding equation 1   &   2 we