Question

How do you solve `x^2-8x-20<0`?

Answer 1

Solve f(x) = x^2 - 8x - 20 < 0
Answer: open interval (-2, 10).

Explanation:

First, solve f(x) = 0.
Find 2 numbers knowing sum (8) and product (-20). Roots have different signs.
Factor pairs of (-20) --> (-1, 20)(-2, 10). This sum is 8 = -b. Then the 2 real roots are: -2 and 10.
Use the test point method and number line to solve f(x) < 0.
Substitute x = 0 into the inequality, we get -20 < 0. It is true, then the origin O is located on the solution set, that is the open interval
(-2, 10).

---------------------|-2====|0=================|10--------------