Question

How do you solve quadratic inequality, graph, and write in interval notation `x^2 - 8x + 15 >0`?

Answer 1

Solve f(x) = x^2 - 8x + 15 > 0
Solution set: open intervals: (-infinity, 3) and (5, +infinity).

Explanation:

First solve f(x) = 0.
Find 2 numbers knowing sum (8) and product (15). Both roots are positive (Rule of Signs)
Factor pairs of (15) -> (1, 15)(3, 5). This sum is 8 = -b. Then, the 2 real roots are: 3 and 5.
Use the number line and origin O as test point. Substitute x = 0 into the inequality. We get 15 > 0. It is true, then O is located on the solution set that are the 2 rays.
Solution set is the open intervals (-infinity, 3) and (5, +infinity)

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