Solve the following quadratic inequality x 2 - ... - JAMB Mathematics 2023 Question

Let's solve the quadratic inequality:

\[ x^2 - x - 4 \leq 2 \]

First, bring all terms to one side to form a quadratic expression:

\[ x^2 - x - 6 \leq 0 \]

Now, factor the quadratic expression:

\[ (x - 3)(x + 2) \leq 0 \]

Now, identify the intervals where this expression is less than or equal to zero by considering the signs of the factors:

1. When \( x - 3 \leq 0 \) and \( x + 2 \geq 0 \):
   - \( x \leq 3 \)
   - \( x \geq -2 \)

2. When \( x - 3 \geq 0 \) and \( x + 2 \leq 0 \):
   - \( x \geq 3 \)
   - \( x \leq -2 \)

Combine the intervals:

\[ -2 \leq x \leq 3 \]