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

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Question: If one root of the equation x^2 - 6x + k = 0 is 2, what is the value of k?

Options:

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

Correct Answer: 4

Solution: 

Using the root, we substitute: 2^2 - 6*2 + k = 0 => 4 - 12 + k = 0 => k = 8.

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

Practice Questions

Q1
If one root of the equation x^2 - 6x + k = 0 is 2, what is the value of k?
  1. 4
  2. 6
  3. 8
  4. 10

Questions & Step-by-Step Solutions

If one root of the equation x^2 - 6x + k = 0 is 2, what is the value of k?
  • Step 1: Start with the equation x^2 - 6x + k = 0.
  • Step 2: We know that one root of the equation is 2.
  • Step 3: Substitute 2 into the equation for x: 2^2 - 6*2 + k = 0.
  • Step 4: Calculate 2^2, 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 4 - 12, which equals -8. So now we have: -8 + k = 0.
  • Step 8: To find k, add 8 to both sides of the equation: k = 8.
  • Quadratic Equations – Understanding how to substitute a known root into a quadratic equation to find an unknown coefficient.
  • Substitution Method – Using substitution to simplify and solve for unknown variables in equations.
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