# How do you solve the inequality #2x^2+9x+3<=0#?

##### 3 Answers

#### Explanation:

graph{2x^2+9x+3 [-10, 10, -5, 5]}

I personally like to visualize the inequality, and think "where is the graph of

#### Explanation:

Reorganizing,

graph{2x^2+9x+3 < 0 [-10, 10, -5, 5]}

interval [-0.414, -0.36]

#### Explanation:

First solve this quadratic equation and find its 2 real roots by using the improved quadratic formula (Socratic Search);

There are 2 real roots:

Since a = 2 > 0, the parabola graph opens upward. Between the 2 real roots, f(x) < 0, as one part of the graph stays below the x-axis.

There for f(x) < 0 between the 2 real roots.

Answer by closed interval: [- 4.14, 0.36]

Both end points (-0.36 and -4.14) are included in the solution set.

Graph on the Number Line:

-------------------- -4.14 ============= -0.36 ---- 0 ----------------------