Root-Coefficent Relationships(4)
2007-11-11 9:14 pm
Given that x2-2x-5=0 has 2 different roots, and x2+ax+b=0 has 2 roots, each 2 less than the corresponding root of the equation, find the values of a and b.
回答 (1)
2007-11-11 9:18 pm
✔ 最佳答案
Let a and b be the roots of the equation x2-2x-5=0a+b = 2, ab = -5
(a-2)+ (b-2) = (a+b) - 4 = 2-4 = -2
(a-2)(b-2) = ab - 2(a+b) + 4 = -5-2(2) + 4 = -5
The equation is x^2 + 2x - 5 = 0
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