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Which of the following is true about the roots of the polynomial x^2 + 4x + 4?

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

Options:

  1. It has two distinct real roots.
  2. It has one real root with multiplicity 2.
  3. It has no real roots.
  4. It has two complex roots.

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

Solution: 

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

Which of the following is true about the roots of the polynomial x^2 + 4x + 4?

Practice Questions

Q1
Which of the following is true about the roots of the polynomial x^2 + 4x + 4?
  1. It has two distinct real roots.
  2. It has one real root with multiplicity 2.
  3. It has no real roots.
  4. It has two complex roots.

Questions & Step-by-Step Solutions

Which of the following is true about the roots of the polynomial x^2 + 4x + 4?
  • Step 1: Identify the polynomial given in the question, which is x^2 + 4x + 4.
  • Step 2: Look for a way to factor the polynomial. We want to express it as (x + a)(x + b).
  • Step 3: Notice that the polynomial can be rewritten as (x + 2)(x + 2) because 2 + 2 = 4 and 2 * 2 = 4.
  • Step 4: Since (x + 2)(x + 2) is the same as (x + 2)^2, we see that the polynomial has a repeated factor.
  • Step 5: This means that the polynomial has one real root, which is x = -2, and it occurs twice (this is called multiplicity 2).
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