2019 · Q19
If the equations x² + 5x + 6 = 0 and x² + kx + 1 = 0 have a common root, then what is the value of k?
Elementary MathematicsAlgebra
- A-5/2 or -10/3
- B5/2 or 10/3
- C5/2 or -10/3
- D-5/2 or 10/3
Explanation
x^2+5x+6 = 0 has roots -2 and -3. Substituting x = -2 in x^2+kx+1 = 0 gives 4-2k+1 = 0, k = 5/2; substituting x = -3 gives 9-3k+1 = 0, k = 10/3.