The number of pairs a , b of real numbers, such that whenever α is a root of the equation x 2 + a x + b = 0 , α 2 - 2 is also a root of this equation, is :

Step-by-step solution

Consider the equation x 2 + a x + b = 0 It has two roots (not necessarily real α and β ) Either α = β or α ≠ β Case (1) If α = β , then it is repeated root. Given than α 2 - 2 is also root So, α = α 2 - 2 ⇒     α + 1 α - 2 = 0 ⇒   α = - 1 or α = 2 When α = - 1 then a , b = 2 , 1 α = 2 then a , b = - 4 , 4 Case (2) If α ≠ β , then four possibilities are there (I) α = α 2 - 2