Question

List the elements of the following sets:

{x : x² – 2x – 3 = 0}

Answer 1

{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