JAMB 2014 · UTME · Q21✱✱

A binary operation $*$ is defined by $x * y = xy$ . If $x * x = 12 - x$ , find the possible values of $x$ .

Worked solution (try it first)

$x * x = x \times x = x^2$ , so the equation is $x^2 = 12 - x$ .
Bring everything to one side: $x^2 + x - 12 = 0$ , which factorises as $(x - 3)(x + 4) = 0$ .
So $x = 3$ or $x = -4$ , option C.