Advanced MathMediumCompleting a square: sum of the constants
Advanced Math practice question
The expression x² + 4x + c is equal to (x + a)² for all values of x, where a and c are constants. What is the value of a + c?
Answer: 6
(x + a)² = x² + 2ax + a². Matching 2a = 4 gives a = 2, and c = a² = 4. So a + c = 6.
Common wrong answers
- If you answered 4
- 4 is c alone.
- If you answered 8
- 8 comes from a = 4, matching a to the x coefficient without halving.
- If you answered 20
- 20 comes from a = 4 and c = 16.
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