Question

How do you solve `(x + 13)(x - 19)>=0`?

Answer 1

Answer: `x in (-oo;-13> uu <19;+oo)`

Explanation:

From tjhe inequality you can see, that your function has 2 zeros: `x_1=-13` and `x_2=19` and the function takes positive values when `x` goes to `+oo` and `-oo`

graph{x^2-6x-247 [-40, 40, -20, 20]}

so you can write the solution: `x in (-oo;-13> uu <19;+oo)`

Answer 2

Solve `(x + 13)(x - 19) >= 0`

Ans: (-infinity, -13] and [19, infinity)

Explanation:

The 2 x-intercepts (real roots) are x = -13 and x = 19.
Use the algebraic method to solve the inequality `f(x) >= 0`. Between the 2 real roots f(x) < 0 as opposite to the side of a = 1.. Outside the interval (-13, 19), `f(x) >= 0.`
Answer by half closed intervals: (-infinity, -13] and [19, infinity).
The critical points (-13) and (19) are included in the solution set.