Question
List the elements of the following sets: ${x : x^2 – 2x – 3 = 0}$
✓
Answer
${x : x^2 – 2x – 3 = 0}$
$x^2 - 2x - 3 = 0$
$\Rightarrow x^2 - 3x + x - 3 = 0$
$\Rightarrow x (x-3) + 1 (x-3) = 0$
$\Rightarrow (x+1) (x - 3) = 0$
$\therefore $ Either $x - 3 = 0 x$
$x = 3$ Or $x + 1 = 0$
$x = -1$
$\therefore $ Elements of the set ${x : x^2 - 2x - 3 = 0}$ are $3$ and $-1$
$x^2 - 2x - 3 = 0$
$\Rightarrow x^2 - 3x + x - 3 = 0$
$\Rightarrow x (x-3) + 1 (x-3) = 0$
$\Rightarrow (x+1) (x - 3) = 0$
$\therefore $ Either $x - 3 = 0 x$
$x = 3$ Or $x + 1 = 0$
$x = -1$
$\therefore $ Elements of the set ${x : x^2 - 2x - 3 = 0}$ are $3$ and $-1$
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