2026 · Q13
If 5 is a root of the equation x²+px−55 = 0 and the quadratic equation x²+px+k = 0 has equal roots, then what is the value of k?
Elementary MathematicsAlgebra
- A3
- B6
- C9
- D12
Explanation
Substituting x = 5 into x² + px − 55 = 0 gives 25 + 5p − 55 = 0, so p = 6. For the equation x² + 6x + k = 0 to have equal roots, its discriminant must vanish. Setting 36 − 4k = 0 gives k = 9, option C.