# Which graph represents the solution set for the quadratic inequality x^{2} + 2x + 1 > 0?

Quadratic equations are a very important type of equation that has a degree of two. They have many applications.

## Answer: The given quadratic inequality x^{2} + 2x + 1 > 0 has its solution: (-∞, -1) ∪ (-1, ∞)

Let's understand the solution in detail.

**Explanation:**

First, we convert the inequality into factored form.

⇒ x^{2} + 2x + 1 > 0

Now, using the algebraic identity of (a + b)^{2 }= a^{2} + 2ab + b^{2}, we get (x + 1)^{2} = x^{2} + 2x +1

⇒ (x + 1)^{2} > 0

⇒ |x + 1| > 0

Now, from the above equation, we can have x + 1 > 0 or x + 1 < 0, or x > -1 or x < -1.

Hence, the solution to the quadratic inequality is (-∞, -1) ∪ (-1, ∞) or the entire cartesian plane except for the point (-1, 0).

The graph of the function is shown above. Note that, (-1, 0) is not included in the solution.

### Hence, the solution of the given equality is (-∞, -1) ∪ (-1, ∞).

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