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The equation x^2 - 9 = 0 has roots that are: (2019)

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Question: The equation x^2 - 9 = 0 has roots that are: (2019)

Options:

  1. -3 and 3
  2. 0 and 9
  3. 3 and 9
  4. 1 and -1

Correct Answer: -3 and 3

Exam Year: 2019

Solution: 

Factoring gives (x-3)(x+3)=0, hence the roots are -3 and 3.

The equation x^2 - 9 = 0 has roots that are: (2019)

Practice Questions

Q1
The equation x^2 - 9 = 0 has roots that are: (2019)
  1. -3 and 3
  2. 0 and 9
  3. 3 and 9
  4. 1 and -1

Questions & Step-by-Step Solutions

The equation x^2 - 9 = 0 has roots that are: (2019)
  • Step 1: Start with the equation x^2 - 9 = 0.
  • Step 2: Recognize that x^2 - 9 is a difference of squares, which can be factored.
  • Step 3: Factor the equation into (x - 3)(x + 3) = 0.
  • Step 4: Set each factor equal to zero: x - 3 = 0 and x + 3 = 0.
  • Step 5: Solve the first equation: x - 3 = 0 gives x = 3.
  • Step 6: Solve the second equation: x + 3 = 0 gives x = -3.
  • Step 7: The roots of the equation are -3 and 3.
  • Quadratic Equations – Understanding how to solve quadratic equations using factoring.
  • Roots of Equations – Identifying the roots of a polynomial equation.
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