# How do you solve the inequality #x^2 + 2x - 3 <=0#?

##### 2 Answers

Feb 21, 2016

First calculate the zeros of the polynom:

So the inequality can be simplified into:

This will happen when one of the factors is positive and the other negative, so the solution will be:

Feb 22, 2016

Closed Interval [-3, 1]

#### Explanation:

First , solve f(x) = 0.

Since a + b + c = 0, use shortcut. One real root is 1 and the other is c/a = -3.

Use the algebraic method to solve f(x) <= 0. Between the 2 real roots (x-intercepts), f(x) < 0. (The parabola graph is below the x-axis because a > 0)).

Solution set: closed interval [-3, 1].

The 2 end points ( -3 and 1) are included in the solution set.