16Hit1600
Advanced MathVery hardPerfect-square trinomial constants

Advanced Math practice question

If 4x² − 20x + c = (2x − a)² for all values of x, where a and c are positive constants, what is the value of a + c?

Answer: 30

(2x − a)² = 4x² − 4ax + a². Matching −4a = −20 gives a = 5, and c = a² = 25. So a + c = 30.

Common wrong answers

If you answered 10
10 takes a = 5 and c = 5, forgetting to square.
If you answered 15
15 uses a = 10 and c = 5 from mismatched coefficients.
If you answered 25
25 is c alone.

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