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

Question

The number of quadratic equations that are unchanged by squaring their roots is, 2, 4, 6, 8

MARKS App · Accepted Answer

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

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