F.4 QUADRATIC EQUATIONS
2013-10-09 5:53 am
If α and β are the roots of the equation x2 + bx + c = 0, and α + 2 and β + 2 are the roots of the equation x2 + cx + b = 0, find the values of b and c.
回答 (1)
2013-10-09 6:18 am
✔ 最佳答案
α + β = -b...(1)αβ = c...(2)
α + 2 + β + 2 = -c...(3)
(α + 2)(β + 2) = b...(4)
From 4, αβ + 2(α + β) + 4 = b
c - 2b + 4 = b
c = 3b - 4
From (3) 4 - b = -c => b = c + 4
So, c = 3(c + 4) - 4 or c = -4
b = 0
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