Answer:
Option 4: (3,5)
Step-by-step explanation:
(x - 3)(x - 5) < 0
Therefore, the intervals that must be tested are x < 3 , 3<x<5 and x>5
Test of the interval x<3⇒ Let x = 0 ⇒ (-3)(-5) = 15 > 0
Test of the interval 3<x<5 ⇒ Let x = 4 ⇒ (4-3)(4-5) = (1)(-1) = -1 < 0
Test of the interval x>5⇒ Let x = 6 ⇒ (6-3)(6-5) = (3)(1) = 3 > 0
So, the solution set for the quadratic inequality is the interval 3<x<5
Or x ∈ (3,5)
See the attached figure.
The answer is option 4
