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If one root of the equation x² - 7x + k = 0 is 3, find k. (2023)

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Question: If one root of the equation x² - 7x + k = 0 is 3, find k. (2023)

Options:

  1. 10
  2. 12
  3. 15
  4. 9

Correct Answer: 10

Solution: 

Using the root, substitute x = 3: 3² - 7*3 + k = 0, which gives k = 10.

If one root of the equation x² - 7x + k = 0 is 3, find k. (2023)

Practice Questions

Q1
If one root of the equation x² - 7x + k = 0 is 3, find k. (2023)
  1. 10
  2. 12
  3. 15
  4. 9

Questions & Step-by-Step Solutions

If one root of the equation x² - 7x + k = 0 is 3, find k. (2023)
  • Step 1: Start with the equation x² - 7x + k = 0.
  • Step 2: We know that one root of the equation is 3.
  • Step 3: Substitute x = 3 into the equation: 3² - 7*3 + k = 0.
  • Step 4: Calculate 3², which is 9.
  • Step 5: Calculate 7*3, which is 21.
  • Step 6: Now the equation looks like: 9 - 21 + k = 0.
  • Step 7: Simplify the left side: 9 - 21 = -12, so we have -12 + k = 0.
  • Step 8: To find k, add 12 to both sides: k = 12.
  • 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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