Question

solve the inequality: \\(s^2 > 2s - 8\\)

interval notation solution:
no solution

Explanation:

Step 1: Rearrange the inequality

Move all terms to one side.

$$s^2 - 2s + 8 > 0$$

Step 2: Analyze the discriminant

Find the discriminant of the quadratic expression.

$$D = (-2)^2 - 4(1)(8) = 4 - 32 = -28$$

Step 3: Determine the solution set

Since \(D < 0\) and the leading coefficient is positive, the inequality holds for all real numbers.

$$(-\infty, \infty)$$

Answer:

Interval notation solution: \((-\infty, \infty)\)