Which graph represents the solution set for the quadratic inequality x2 + 2x + 1 > 0?
Solution:
Quadratic equations are a very important type of equation that has a degree of two. They have many applications.
First, we convert the inequality into factored form.
⇒ x2 + 2x + 1 > 0
Now, using the algebraic identity of (a + b)2 = a2 + 2ab + b2, we get (x + 1)2 = x2 + 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, ∞).
Which graph represents the solution set for the quadratic inequality x2 + 2x + 1 > 0?
Summary:
The given quadratic inequality x2 + 2x + 1 > 0 has its solution: (-∞, -1) ∪ (-1, ∞)