# How do you solve the quadratic inequality #x^2-9x +18 >0#?

##### 2 Answers

#### Explanation:

When

When

When

Putting these together:

for

graph{x^2-9x+18 [-5.71, 14.29, -3.68, 6.32]}

Solve f(x) = x^2 - 9x + 18 > 0

Ans: (-infinity, 3) and (5, infinity)

#### Explanation:

First, solve f(x) = x^2 - 9x + 18 = 0.

Roots have same sign. Factor pairs of (18) --> (2, 9)(3, 6). This sum is 9 = -b. Then the 2 real roots are: 3 and 6.

Use the algebraic method to solve f(x) > 0. Between the 2 real roots

(3) and (5), f(x) < 0 as opposite to the sign of a = 1. f(x) is positive (> 0) outside the interval (3, 5).

Answer by open intervals: (-infinity, 3) and (5, infinity)