JAMB Mathematics 2023 Paper

$x^2 - x - 4 \le 2$

Subtract two from both sides to rewrite it in the quadratic standard form:= $x^2 - x - 4 - 2 \le 2 - 2$= $x^2 - x - 6 \le 0$Now set it = 0 and factor and solve like normal.= $x^2 - x$ - 6=0= $(x - 3)(x + 2)$=0$x$ + 2 = 0 or $x$ - 3 = 0$x$ = -2 or $x$ = 3So the two zeros are -2 and 3, and will mark the boundaries of our answer interval. To find out if the interval is between -2 and 3, or on either side, we simply take a test point between -2 and 3 (for instance, $x$ = 0) and evaluate the original inequality.= $x2 - x - 4 \le 2$= $(0)^2 - (0) - 4 \le 2$= $0 - 0 - 4 \le 2$$-4 \le 2$Since the above is a true statement, we know that the solution interval is between -2 and 3, the same region where we picked our test point. Since the original inequality was less than or equal, we include the endpoints.∴ $-2 \le x \le 3.$