Which of the following is true about the roots of the polynomial P(x) = x^2 + 4x

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Question: Which of the following is true about the roots of the polynomial P(x) = x^2 + 4x + 4?

Options:

Correct Answer: It has one real root with multiplicity 2.

Solution:

The polynomial can be factored as (x + 2)^2, indicating it has one real root with multiplicity 2.

Which of the following is true about the roots of the polynomial P(x) = x^2 + 4x + 4?

Which of the following is true about the roots of the polynomial P(x) = x^2 + 4x + 4?

Step 1: Identify the polynomial given in the question, which is P(x) = x^2 + 4x + 4.
Step 2: Recognize that this is a quadratic polynomial, which can be expressed in the standard form ax^2 + bx + c.
Step 3: Look for a way to factor the polynomial. Notice that the expression can be rewritten as (x + 2)(x + 2).
Step 4: This means that the polynomial can be factored as (x + 2)^2.
Step 5: Understand that when a polynomial is factored like this, it indicates that there is a repeated root.
Step 6: The root of the equation (x + 2) = 0 is x = -2.
Step 7: Since the factor (x + 2) appears twice, we say that the root x = -2 has a multiplicity of 2.
Step 8: Conclude that the polynomial P(x) = x^2 + 4x + 4 has one real root, which is -2, and it occurs twice.

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