Solve x^2 + 2x + 5 < 0

Step by step

The question

Question: solve x² + 2x + 5 < 0.

There is an x², so the answer can be two parts.

1 Does it cross 0?

It does not factor.

Let's look at b² − 4ac, the part under the root in the formula.

It is −16, negative.

Negative under the root: no x makes it 0.

So it never crosses 0: it is always plus, or always minus.

Test one number, x = 0: it gives 5.

Plus.

So it is always plus.

2 Read the answer

It is always plus, never less than 0.

So there is no solution.

Let's look back.

First: does it cross 0?.

Last: read the answer.