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Question
Write the following sets in the roaster form:
F = {x | x4 – 5x2 + 6 = 0, x ∈ R}
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Solution
Given: F = {x | x4 – 5x2 + 6 = 0, x ∈ R}
To find: Roster form of given set
x4 – 5x2 + 6 = 0
⇒ x4 – 3x2 – 2x2 + 6 = 0
⇒ x2(x2 – 3) – 2(x2 – 3) = 0
⇒ (x2 – 3)(x2 – 2) = 0
⇒ x2 = 3 or 2
⇒ x = `+- sqrt(3)` or `+- sqrt(2)`
⇒ x = `sqrt(3), - sqrt(3), sqrt(2)` or `- sqrt(2)`
So, F = `{- sqrt(3), - sqrt(2), sqrt(2), sqrt(3)}`
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