Question

How do you solve the quadratic inequality `x^2 -4x -5 <0`?

Answer 1

f(x) = x^2 - 4x - 5 < 0

First, find the 2 real roots: f(x) = 0.
Since a -b + c = 0, one real root is (-1) and the other is (-c/a = 5)

------------------|-1===|0===========|5-----------------

Test point method . Plot (-1) and (5) on the number line. Use the origin O as test point --> x = 0 --> f (x) = -5 < 0. True. Then the origin O is located on the segment (-1, 5) that is the solution set.
Answer: Open interval (-1, 5).

Algebraic Method . Between the 2 real roots (-1) and (5), f(x) is negative, having the opposite sign to a (> 0).
Answer: Open interval (-1, 5)