Question

I need this for quadratic inequalities

Answer 1

(3, 5 )

Explanation:

Given that the intervals to be tested are

x < 3, 3 < x < 5, x > 5

Choose test points within each interval, evaluate and compare

For x < 3

Choose x = 0, thus

(0 - 3)(0 - 5) = (- 3)(- 5) = 15 > 0 ← solution not in this interval

For 3 < x < 5

Choose x = 4

(4 - 3)(4 - 5) = (1)(- 1) = - 1 < 0 ← solution in this interval

For x > 5

Choose x = 6

(6 - 3)(6 - 5) = (3)(1) = 3 > 0 ← solution not in this interval

Thus the solution to (x - 3)(x - 5) < 0 is

3 < x < 5, that is (3, 5)

Answer 2

Option C is correct