Final answer:
The solution to the quadratic inequality x²−2x−48>0 is found by factoring and testing intervals around the roots. In interval notation, the solution is (-∞, -6) ∪ (8, +∞), which corresponds to option (a): x < -6 or x > 8.
Step-by-step explanation:
To solve the quadratic inequality x²−2x−48>0, we first factor the quadratic expression. The expression can be factored into (x + 6)(x - 8) > 0. This means the product of (x + 6) and (x - 8) is greater than zero. To find the intervals where this inequality holds true, we consider the values x = -6 and x = 8, which are the roots of the quadratic equation.
We test intervals defined by these roots: (-∞, -6), (-6, 8), and (8, +∞). We find that the inequality is satisfied for x < -6 and x > 8. Therefore, in interval notation, the solution set is (-∞, -6) ∪ (8, +∞).
The correct answer matches option (a): x < -6 or x > 8.