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If the quadratic equation x^2 + 4x + c = 0 has one root equal to -2, what is the

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Question: If the quadratic equation x^2 + 4x + c = 0 has one root equal to -2, what is the value of c?

Options:

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

Correct Answer: 0

Solution: 

If one root is -2, then substituting x = -2 gives: (-2)^2 + 4(-2) + c = 0 => 4 - 8 + c = 0 => c = 4.

If the quadratic equation x^2 + 4x + c = 0 has one root equal to -2, what is the

Practice Questions

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

Questions & Step-by-Step Solutions

If the quadratic equation x^2 + 4x + c = 0 has one root equal to -2, what is the value of c?
Correct Answer: 4
  • Step 1: Start with the quadratic equation: x^2 + 4x + c = 0.
  • Step 2: We know one root of the equation is -2.
  • Step 3: Substitute -2 for x in the equation: (-2)^2 + 4(-2) + c = 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 + c = 0.
  • Step 7: Simplify 4 - 8, which equals -4. So now we have: -4 + c = 0.
  • Step 8: To find c, add 4 to both sides of the equation: c = 4.
  • Quadratic Equations – Understanding the structure of quadratic equations and how to find coefficients based on given roots.
  • Substitution – Using substitution to find unknown values by plugging in known values into the equation.
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