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If one root of the equation x^2 - 4x + k = 0 is 2, what is the value of k?

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Question: If one root of the equation x^2 - 4x + k = 0 is 2, what is the value of k?

Options:

  1. 0
  2. 2
  3. 4
  4. 6

Correct Answer: 4

Solution: 

Substituting x=2 into the equation gives 2^2 - 4*2 + k = 0, thus k = 4.

If one root of the equation x^2 - 4x + k = 0 is 2, what is the value of k?

Practice Questions

Q1
If one root of the equation x^2 - 4x + k = 0 is 2, what is the value of k?
  1. 0
  2. 2
  3. 4
  4. 6

Questions & Step-by-Step Solutions

If one root of the equation x^2 - 4x + k = 0 is 2, what is the value of k?
  • Step 1: Start with the equation x^2 - 4x + k = 0.
  • Step 2: We know that one root of the equation is 2.
  • Step 3: Substitute x = 2 into the equation: 2^2 - 4*2 + k = 0.
  • Step 4: Calculate 2^2, which is 4.
  • Step 5: Calculate -4*2, which is -8.
  • Step 6: Now the equation looks like: 4 - 8 + k = 0.
  • Step 7: Simplify the left side: 4 - 8 equals -4, so we have -4 + k = 0.
  • Step 8: To find k, add 4 to both sides of the equation: k = 4.
  • Quadratic Equations – Understanding how to substitute values into a quadratic equation to find unknown coefficients.
  • Roots of Equations – Identifying and using the roots of a quadratic equation to solve for parameters.
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