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For the quadratic equation x^2 - 6x + k = 0 to have one root equal to 3, what is

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Question: For the quadratic equation x^2 - 6x + k = 0 to have one root equal to 3, what is the value of k? (2023)

Options:

  1. 3
  2. 6
  3. 9
  4. 12

Correct Answer: 9

Exam Year: 2023

Solution: 

If one root is 3, then substituting x = 3 gives 3^2 - 6*3 + k = 0, leading to k = 9.

For the quadratic equation x^2 - 6x + k = 0 to have one root equal to 3, what is

Practice Questions

Q1
For the quadratic equation x^2 - 6x + k = 0 to have one root equal to 3, what is the value of k? (2023)
  1. 3
  2. 6
  3. 9
  4. 12

Questions & Step-by-Step Solutions

For the quadratic equation x^2 - 6x + k = 0 to have one root equal to 3, what is the value of k? (2023)
  • Step 1: Start with the quadratic equation x^2 - 6x + k = 0.
  • Step 2: We know that one root of the equation is 3.
  • Step 3: Substitute x = 3 into the equation: 3^2 - 6*3 + k = 0.
  • Step 4: Calculate 3^2, which is 9.
  • Step 5: Calculate -6*3, which is -18.
  • Step 6: Now the equation looks like: 9 - 18 + k = 0.
  • Step 7: Simplify the left side: 9 - 18 equals -9, so we have -9 + k = 0.
  • Step 8: To find k, add 9 to both sides: k = 9.
  • Quadratic Equations – Understanding the properties of quadratic equations and how to find roots.
  • Substitution Method – Using substitution to find unknown parameters in equations.
  • Discriminant – Recognizing that a quadratic equation can have one root when the discriminant is zero.
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