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If the quadratic equation x^2 + 5x + k = 0 has one root as 2, what is the value

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Question: If the quadratic equation x^2 + 5x + k = 0 has one root as 2, what is the value of k? (2019)

Options:

  1. 6
  2. 8
  3. 10
  4. 12

Correct Answer: 6

Exam Year: 2019

Solution: 

Substituting x = 2 into the equation gives 2^2 + 5(2) + k = 0, leading to 4 + 10 + k = 0, thus k = -14.

If the quadratic equation x^2 + 5x + k = 0 has one root as 2, what is the value

Practice Questions

Q1
If the quadratic equation x^2 + 5x + k = 0 has one root as 2, what is the value of k? (2019)
  1. 6
  2. 8
  3. 10
  4. 12

Questions & Step-by-Step Solutions

If the quadratic equation x^2 + 5x + k = 0 has one root as 2, what is the value of k? (2019)
  • Step 1: Start with the quadratic equation x^2 + 5x + k = 0.
  • Step 2: We know one root of the equation is 2. This means we can substitute x with 2.
  • Step 3: Substitute x = 2 into the equation: 2^2 + 5(2) + k = 0.
  • Step 4: Calculate 2^2, which is 4.
  • Step 5: Calculate 5(2), which is 10.
  • Step 6: Now, rewrite the equation with these values: 4 + 10 + k = 0.
  • Step 7: Combine 4 and 10 to get 14: 14 + k = 0.
  • Step 8: To find k, subtract 14 from both sides: k = -14.
  • Quadratic Equations – Understanding the structure of quadratic equations and how to find unknown coefficients using known roots.
  • Substitution Method – Using substitution to solve for unknown variables by plugging in known values.
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