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If one root of the equation x^2 + 3x + k = 0 is 2, what is the value of k?

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Question: If one root of the equation x^2 + 3x + k = 0 is 2, what is the value of k?

Options:

  1. -4
  2. -6
  3. -5
  4. -3

Correct Answer: -6

Solution: 

Substituting x=2 into the equation gives 2^2 + 3*2 + k = 0, which simplifies to k = -10.

If one root of the equation x^2 + 3x + k = 0 is 2, what is the value of k?

Practice Questions

Q1
If one root of the equation x^2 + 3x + k = 0 is 2, what is the value of k?
  1. -4
  2. -6
  3. -5
  4. -3

Questions & Step-by-Step Solutions

If one root of the equation x^2 + 3x + k = 0 is 2, what is the value of k?
  • Step 1: Start with the equation x^2 + 3x + k = 0.
  • Step 2: We know that one root of the equation is 2.
  • Step 3: Substitute x = 2 into the equation: 2^2 + 3*2 + k = 0.
  • Step 4: Calculate 2^2, which is 4.
  • Step 5: Calculate 3*2, which is 6.
  • Step 6: Now the equation looks like 4 + 6 + k = 0.
  • Step 7: Combine 4 and 6 to get 10, so the equation is now 10 + k = 0.
  • Step 8: To find k, subtract 10 from both sides: k = -10.
  • 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 unknowns.
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