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If the quadratic equation x^2 + 4x + c = 0 has one root equal to -2, what is the
If the quadratic equation x^2 + 4x + c = 0 has one root equal to -2, what is the value of c?
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Q1
If the quadratic equation x^2 + 4x + c = 0 has one root equal to -2, what is the value of c?
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If one root is -2, then substituting x = -2 gives: (-2)^2 + 4(-2) + c = 0 => 4 - 8 + c = 0 => c = 4.
Questions & Step-by-step Solutions
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Q: If the quadratic equation x^2 + 4x + c = 0 has one root equal to -2, what is the value of c?
Solution:
If one root is -2, then substituting x = -2 gives: (-2)^2 + 4(-2) + c = 0 => 4 - 8 + c = 0 => c = 4.
Steps: 8
Show Steps
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.
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