Quadratic Inequality

[mathdad]

Solve the inequality.

x^2 - x - 6 < 0

Here I go.

Replace < with the = sign, set to 0 and factor.

(x - 3)(x + 2) = 0

x = 3 and x = - 2

Between -2 and 3, the function will always be greater than 0 or always less than 0.

I will pick a number between
-2 & 3. How about 0? I love using 0 as a substitute value.

Let x = 0

x^2 - x - 6 < 0

(0)^2 - 0 - 6 < 0

- 6 < 0

I understand this to mean that the given function is less than 0 between -2 and 3.

I conclude from this finding that x^2 - x - 6 is less than 0 in the interval (-2, 3).

So, how did I do?

 

[MarkFL]

We know the quadratic expression will have a parabolic graph that opens upwards, and so it must be negative in the open interval between its roots:

\((-2,3)\)

I agree with your conclusion.

 

[mathdad]

We know the quadratic expression will have a parabolic graph that opens upwards, and so it must be negative in the open interval between its roots:

\((-2,3)\)

I agree with your conclusion.

Cool. Another one for the books.