If the roots of the equation x^{2}-bx+c=5 differ by 5, then which one of the following is correct?
- A. b^{2}=4c+5 ✓
- B. c^{2}=4b-5
- C. b^{2}+c^{2}=5
- D. b^{2}-c^{2}=5
Correct Answer: A. b^{2}=4c+5
Explanation
Rewrite as x^2 - bx + (c-5) = 0. Difference of roots is \frac{\sqrt{b^2 - 4ac}}{a} = 5. Thus, \sqrt{b^2 - 4(1)(c-5)} = 5, giving b^2 - 4c + 20 = 25, or b^2 = 4c + 5.
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