# How do you solve #-2x^2+6X+15 <=0#?

##### 1 Answer

Jun 5, 2016

#### Answer:

Half closed intervals: (-inf., x2] and [x1, inf.)

#### Explanation:

First, solve f(x) = 0 to find the 2 real roots. Use the improved quadratic formula (Socratic Search)

There are 2 real roots (2 x-intercepts):

Since a < 0, the parabola opens downward.

f(x) > 0 inside the interval (x2, x1), between the 2 x-intercepts.

f(x) < 0 outside the (x2, x1) interval, because the 2 parabola branches are below the x-axis.

Solution set: Two half-closed intervals (-inf., x2] and [x1, inf.)

The 2 end points x1 and x2 are include in the solution set