The roots of the equation x^2 + 2x + 1 = 0 are:

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Question: The roots of the equation x^2 + 2x + 1 = 0 are:

Options:

Correct Answer: -1

Solution:

The equation can be factored as (x + 1)^2 = 0, giving a double root at x = -1.

The roots of the equation x^2 + 2x + 1 = 0 are:

The roots of the equation x^2 + 2x + 1 = 0 are:

Step 1: Start with the equation x^2 + 2x + 1 = 0.
Step 2: Recognize that this is a quadratic equation in the form of ax^2 + bx + c.
Step 3: Identify the coefficients: a = 1, b = 2, c = 1.
Step 4: Look for two numbers that multiply to 'c' (1) and add to 'b' (2).
Step 5: The numbers 1 and 1 work because 1 * 1 = 1 and 1 + 1 = 2.
Step 6: Rewrite the equation using these numbers: (x + 1)(x + 1) = 0.
Step 7: This can be simplified to (x + 1)^2 = 0.
Step 8: To find the roots, set (x + 1) = 0.
Step 9: Solve for x: x + 1 = 0 gives x = -1.
Step 10: Since it's (x + 1)^2, this root is a double root.

Quadratic Equations – Understanding how to solve quadratic equations using factoring and recognizing the nature of roots.
Factoring – Ability to factor quadratic expressions and identify roots from factored forms.
Double Roots – Recognizing that a perfect square trinomial results in a double root.