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

##### 1 Answer

Jul 2, 2015

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)

===========|0=========|3--------------|5===============