2023 · Q44
For what values of m, is mx² + mx + 8x + 9 a perfect square?
Elementary MathematicsAlgebra
- A1, 4
- B4, 9
- C9, 16
- D4, 16
Explanation
mx² + (m + 8)x + 9 is a perfect square iff its discriminant vanishes: (m + 8)² − 36m = m² − 20m + 64 = (m − 4)(m − 16) = 0. Hence m = 4 or m = 16 (D).