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The quadratic equation x^2 + 6x + 9 = 0 can be expressed in which of the followi

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Question: The quadratic equation x^2 + 6x + 9 = 0 can be expressed in which of the following forms? (2020)

Options:

  1. (x + 3)^2
  2. (x - 3)^2
  3. (x + 6)^2
  4. (x - 6)^2

Correct Answer: (x + 3)^2

Exam Year: 2020

Solution: 

This is a perfect square trinomial: (x + 3)(x + 3) = 0.

The quadratic equation x^2 + 6x + 9 = 0 can be expressed in which of the followi

Practice Questions

Q1
The quadratic equation x^2 + 6x + 9 = 0 can be expressed in which of the following forms? (2020)
  1. (x + 3)^2
  2. (x - 3)^2
  3. (x + 6)^2
  4. (x - 6)^2

Questions & Step-by-Step Solutions

The quadratic equation x^2 + 6x + 9 = 0 can be expressed in which of the following forms? (2020)
  • Step 1: Identify the quadratic equation given, which is x^2 + 6x + 9 = 0.
  • Step 2: Recognize that a perfect square trinomial has the form (a + b)^2 = a^2 + 2ab + b^2.
  • Step 3: In the equation x^2 + 6x + 9, identify a = x and b = 3, since 2ab = 6x and b^2 = 9.
  • Step 4: Rewrite the equation as (x + 3)(x + 3) = 0, which is the same as (x + 3)^2 = 0.
  • Step 5: Conclude that the quadratic equation can be expressed as (x + 3)^2 = 0.
  • Quadratic Equations – Understanding the standard form of quadratic equations and their factorizations.
  • Perfect Square Trinomials – Recognizing and factoring perfect square trinomials.
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