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Question
List the elements of the following sets:
{x : x2 – 2x – 3 = 0}
Solution
{x : x2 – 2x – 3 = 0}
x2 - 2x - 3 = 0
⇒ x2 - 3x + x - 3 = 0
⇒ x (x-3) + 1 (x-3) = 0
⇒ (x+1) (x - 3) = 0
∴ Either x - 3 = 0 x
x = 3
Or
x + 1 = 0
x = -1
∴ Elements of the set {x : x2 - 2x - 3 = 0} are 3 and -1
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