The roots of the equation x^2 + 4x + 4 = 0 are:

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Question: The roots of the equation x^2 + 4x + 4 = 0 are:

Options:

Correct Answer: -2, -2

Solution:

The equation can be factored as (x + 2)^2 = 0, giving a double root at x = -2.

The roots of the equation x^2 + 4x + 4 = 0 are:

The roots of the equation x^2 + 4x + 4 = 0 are:

Step 1: Start with the equation x^2 + 4x + 4 = 0.
Step 2: Look for two numbers that multiply to 4 (the last number) and add to 4 (the middle number).
Step 3: The numbers 2 and 2 work because 2 * 2 = 4 and 2 + 2 = 4.
Step 4: Rewrite the equation using these numbers: (x + 2)(x + 2) = 0.
Step 5: This can be simplified to (x + 2)^2 = 0.
Step 6: To find the roots, set (x + 2) = 0.
Step 7: Solve for x: x + 2 = 0 means x = -2.
Step 8: Since it is (x + 2)^2, this root is a double root.

Quadratic Equations – Understanding how to solve quadratic equations using factoring, completing the square, or the quadratic formula.
Roots and Multiplicity – Identifying the nature of roots, including single and double roots, and their implications on the graph of the equation.