2025 · Q25
If one root of (a-b/2)x^2 - (a+b/2)x + b = 0 is 1, then what is the other root?
Elementary MathematicsAlgebra
- A1
- B2b/(a-b)
- Cb/a
- D(a+b)/(a-b)
Explanation
The equation is ((a-b)/2)x^2-((a+b)/2)x+b=0 (the options disambiguate the bracketing). x=1 is a root: (a-b)/2-(a+b)/2+b=0. Product of roots=b/((a-b)/2)=2b/(a-b), so the other root is 2b/(a-b). Misreading (a-b/2) as a-(b/2) is the trap.