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The roots of the equation x² + 4x + k = 0 are 2 and -6. What is the value of k?

Practice Questions

Q1
The roots of the equation x² + 4x + k = 0 are 2 and -6. What is the value of k? (2021)
  1. -12
  2. -8
  3. -10
  4. -14

Questions & Step-by-Step Solutions

The roots of the equation x² + 4x + k = 0 are 2 and -6. What is the value of k? (2021)
  • Step 1: Identify the given quadratic equation, which is x² + 4x + k = 0.
  • Step 2: Recognize that the roots of the equation are given as 2 and -6.
  • Step 3: Use the formula for the product of the roots, which states that the product of the roots (r1 * r2) is equal to k.
  • Step 4: Calculate the product of the roots: 2 * (-6) = -12.
  • Step 5: Therefore, we find that k = -12.
  • Step 6: To verify, check the sum of the roots: 2 + (-6) = -4, which matches the coefficient of x in the equation (4).
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