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If one root of the equation x² - 6x + k = 0 is 2, find k. (2022)

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Question: If one root of the equation x² - 6x + k = 0 is 2, find k. (2022)

Options:

  1. 8
  2. 10
  3. 12
  4. 6

Correct Answer: 10

Exam Year: 2022

Solution: 

Using the root 2 in the equation: 2² - 6*2 + k = 0, we find k = 10.

If one root of the equation x² - 6x + k = 0 is 2, find k. (2022)

Practice Questions

Q1
If one root of the equation x² - 6x + k = 0 is 2, find k. (2022)
  1. 8
  2. 10
  3. 12
  4. 6

Questions & Step-by-Step Solutions

If one root of the equation x² - 6x + k = 0 is 2, find k. (2022)
  • Step 1: Start with the equation x² - 6x + k = 0.
  • Step 2: We know that one root of the equation is 2.
  • Step 3: Substitute 2 for x in the equation: 2² - 6*2 + k = 0.
  • Step 4: Calculate 2², which is 4.
  • Step 5: Calculate -6*2, which is -12.
  • Step 6: Now the equation looks like: 4 - 12 + k = 0.
  • Step 7: Simplify the left side: 4 - 12 equals -8, so we have -8 + k = 0.
  • Step 8: To find k, add 8 to both sides: k = 8.
  • Quadratic Equations – Understanding how to substitute a known root into a quadratic equation to find an unknown constant.
  • Substitution Method – Using substitution to simplify the process of solving for unknowns in equations.
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