If the roots of the equation x^2 + 6x + 9 = 0 are equal, what is the value of th

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Question: If the roots of the equation x^2 + 6x + 9 = 0 are equal, what is the value of the root? (2023)

Options:

Correct Answer: -3

Exam Year: 2023

Solution:

The equation can be factored as (x+3)(x+3)=0, hence the root is -3.

If the roots of the equation x^2 + 6x + 9 = 0 are equal, what is the value of the root? (2023)

If the roots of the equation x^2 + 6x + 9 = 0 are equal, what is the value of the root? (2023)

Step 1: Identify the equation given, which is x^2 + 6x + 9 = 0.
Step 2: Recognize that the equation is a quadratic equation in the form of ax^2 + bx + c.
Step 3: Check if the roots are equal by calculating the discriminant (b^2 - 4ac). Here, a = 1, b = 6, and c = 9.
Step 4: Calculate the discriminant: (6^2) - (4 * 1 * 9) = 36 - 36 = 0.
Step 5: Since the discriminant is 0, this confirms that the roots are equal.
Step 6: Factor the quadratic equation: x^2 + 6x + 9 can be factored as (x + 3)(x + 3) = 0.
Step 7: Set the factored equation to zero: (x + 3) = 0.
Step 8: Solve for x: x = -3.
Step 9: Conclude that the value of the root is -3.

Quadratic Equations – Understanding the properties of quadratic equations, particularly when the discriminant is zero, indicating equal roots.
Factoring – The ability to factor quadratic expressions to find roots.