If \left(\frac{a-b}{2}\right)x^2 - \left(\frac{a+b}{2}\right)x + b = 0, then what are the roots of this equation?
- A. 1, \frac{b}{a-b}
- B. 1, \frac{2b}{a-b} ✓
- C. 1, \frac{b}{a+b}
- D. 1, \frac{2b}{a+b}
Correct Answer: B. 1, \frac{2b}{a-b}
Explanation
Evaluating the polynomial at x=1 gives \frac{a-b}{2} - \frac{a+b}{2} + b = 0, so 1 is a root. Since the product of the roots is \frac{b}{(a-b)/2} = \frac{2b}{a-b}, the other root must be \frac{2b}{a-b}.
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