What is the root of the equation x² + 6x + 9 = 0?

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Multiple Choice

What is the root of the equation x² + 6x + 9 = 0?

Explanation:
To determine the root of the equation \(x^2 + 6x + 9 = 0\), we can recognize that this is a quadratic equation that can be factored. The equation can be rewritten as: \[ (x + 3)(x + 3) = 0 \] or simply as: \[ (x + 3)^2 = 0. \] Setting \(x + 3\) equal to zero gives: \[ x + 3 = 0 \implies x = -3. \] This shows that \(x = -3\) is the root of the equation. The nature of the quadratic means that this root has a multiplicity of two, indicating it touches the x-axis at this point but does not cross it. Understanding this root is important because it highlights how quadratic equations can sometimes yield a single unique solution rather than two distinct values.

To determine the root of the equation (x^2 + 6x + 9 = 0), we can recognize that this is a quadratic equation that can be factored. The equation can be rewritten as:

[

(x + 3)(x + 3) = 0

]

or simply as:

[

(x + 3)^2 = 0.

]

Setting (x + 3) equal to zero gives:

[

x + 3 = 0 \implies x = -3.

]

This shows that (x = -3) is the root of the equation. The nature of the quadratic means that this root has a multiplicity of two, indicating it touches the x-axis at this point but does not cross it.

Understanding this root is important because it highlights how quadratic equations can sometimes yield a single unique solution rather than two distinct values.

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