The number of quadratic equations that are unchanged by squaring their roots is

Step-by-step solution

α + β = α 2 + β 2 & α β = α 2 β 2 ⇒ α β = 0 or 1 . If α β = 0 , then let, α = 0 ⇒ β = 0 or 1 . If β = 1 α , α + 1 α = α 2 + 1 α 2 = α + 1 α 2 − 2 ⇒ α + 1 α 2 − α + 1 α − 2 = 0 ⇒ α + 1 α = 2 or − 1 ⇒ α = 1 or ω , ω 2 Hence number of such equations are four 0 , 0 , 0 , 1 , 1 , 1 & ω , ω 2