The roots of the equation x² + 4x + 4 = 0 are: (2020)

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Question: The roots of the equation x² + 4x + 4 = 0 are: (2020)

Options:

Correct Answer: -2 and -2

Exam Year: 2020

Solution:

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

The roots of the equation x² + 4x + 4 = 0 are: (2020)

The roots of the equation x² + 4x + 4 = 0 are: (2020)

Step 1: Start with the equation x² + 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)² = 0.
Step 7: Take the square root of both sides: x + 2 = 0.
Step 8: Solve for x by subtracting 2 from both sides: x = -2.

Quadratic Equations – Understanding how to solve quadratic equations using factoring and the quadratic formula.
Roots of Equations – Identifying and interpreting the roots of a quadratic equation, including double roots.