What are the roots of the equation x^2 + 4x + 4 = 0?

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

Options:

Correct Answer: x = -2, -2

Solution:

The equation can be factored as (x + 2)(x + 2) = 0. Thus, the root is x = -2 with multiplicity 2.

What are the roots of the equation x^2 + 4x + 4 = 0?

What are the roots of the equation x^2 + 4x + 4 = 0?

Step 1: Start with the equation x^2 + 4x + 4 = 0.
Step 2: Look for two numbers that multiply to 4 (the constant term) and add to 4 (the coefficient of x).
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 also be written as (x + 2)^2 = 0.
Step 6: To find the roots, set x + 2 = 0.
Step 7: Solve for x: x = -2.
Step 8: Since (x + 2) is squared, the root x = -2 has a multiplicity of 2.

Quadratic Equations – Understanding how to solve quadratic equations using factoring, the quadratic formula, or completing the square.
Roots and Multiplicity – Identifying the roots of a polynomial and understanding the concept of multiplicity in relation to repeated roots.