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For the quadratic equation x^2 + 6x + 8 = 0, what are the roots?

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Question: For the quadratic equation x^2 + 6x + 8 = 0, what are the roots?

Options:

  1. -2 and -4
  2. -4 and -2
  3. 2 and 4
  4. 0 and 8

Correct Answer: -4 and -2

Solution: 

Factoring gives (x+2)(x+4) = 0, hence the roots are -2 and -4.

For the quadratic equation x^2 + 6x + 8 = 0, what are the roots?

Practice Questions

Q1
For the quadratic equation x^2 + 6x + 8 = 0, what are the roots?
  1. -2 and -4
  2. -4 and -2
  3. 2 and 4
  4. 0 and 8

Questions & Step-by-Step Solutions

For the quadratic equation x^2 + 6x + 8 = 0, what are the roots?
Correct Answer: -2 and -4
  • Step 1: Start with the quadratic equation x^2 + 6x + 8 = 0.
  • Step 2: Look for two numbers that multiply to 8 (the constant term) and add up to 6 (the coefficient of x).
  • Step 3: The numbers 2 and 4 work because 2 * 4 = 8 and 2 + 4 = 6.
  • Step 4: Rewrite the equation using these numbers: (x + 2)(x + 4) = 0.
  • Step 5: Set each factor equal to zero: x + 2 = 0 and x + 4 = 0.
  • Step 6: Solve for x in each equation: x = -2 and x = -4.
  • Step 7: The roots of the equation are -2 and -4.
  • Quadratic Equations – Understanding how to solve quadratic equations using factoring.
  • Factoring – Recognizing how to factor a quadratic expression into two binomials.
  • Roots of Equations – Identifying the solutions (roots) of a quadratic equation.
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