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InequalitiesAlgebraHigh schoolabout 0:39

Solve x^2 + 2x + 3 < 0: animated lesson

A narrated, step-by-step inequalities video lesson with captions. Final answer: No solution (∅).

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.2 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
${x}^{2}+2x+3 < 0$
2. Step by step
1. $x^{2} + 2x + 3 < 0$
  Move everything to one side and factor
2. Find the critical points
3. $x \in \varnothing$
  Write the solution set
3. The answer
$\varnothing$
x ∈ No solution (∅)
4. Check
- x = 0: does not satisfy the inequality.

Transcript

The problem. Here is the problem: x squared plus 2x plus 3 less than 0. Solve the inequality and give the answer in interval notation.

Step by step. Move everything to one side and factor. A sign chart needs the form f(x) compared with 0, written as a product/quotient of factors. Find the critical points. There are no real critical points, so the expression keeps one sign for every x. Write the solution set.

The answer. So the answer is No solution (∅). No real number satisfies the inequality.

Check. x equals 0: does not satisfy the inequality.

About inequalities

Solve linear and quadratic inequalities and write the answer as an interval.

Solve x^2 + 2x + 3 < 0: Inequalities Step-by-Step Lesson