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

##### 1 Answer

May 24, 2015

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)