Determine the roots of the equation x² + 6x + 9 = 0. (2023)

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Question: Determine the roots of the equation x² + 6x + 9 = 0. (2023)

Options:

Correct Answer: -3

Exam Year: 2023

Solution:

This is a perfect square: (x + 3)² = 0, hence the root is x = -3.

Determine the roots of the equation x² + 6x + 9 = 0. (2023)

Determine the roots of the equation x² + 6x + 9 = 0. (2023)

Step 1: Identify the equation you need to solve, which is x² + 6x + 9 = 0.
Step 2: Recognize that the equation can be factored. Look for two numbers that multiply to 9 (the last number) and add up to 6 (the middle number).
Step 3: The numbers 3 and 3 work because 3 * 3 = 9 and 3 + 3 = 6.
Step 4: Rewrite the equation using these numbers: (x + 3)(x + 3) = 0.
Step 5: This can be simplified to (x + 3)² = 0.
Step 6: To find the root, set (x + 3) equal to 0: x + 3 = 0.
Step 7: Solve for x by subtracting 3 from both sides: x = -3.

Quadratic Equations – Understanding how to solve quadratic equations, particularly recognizing perfect squares.
Factoring – The ability to factor quadratic expressions to find roots.
Roots of Equations – Identifying the roots of a quadratic equation using various methods.