discriminant問題

2007-05-12 10:15 pm
1. x^2+(a+b)x+ab

discriminate the solution
更新1:

咁佢係2 different real solutions , a repeated real solution定係2 different complex solution

回答 (2)

2007-05-14 2:16 am
✔ 最佳答案
留意根本不須使用discriminant

(x + a)(x + b) = x^2+(a+b)x+ab

所以如果

a 是real, b 是real, a =/= b 就係 2 different real solutions
a 是real, b 是real, a = b 就係 a repeated real solution
a 是complex, b 是complex, a =/= b 就係 2 different complex solutions

還有其它可能的,如a是complex, b是real就會有1 complex 1 real,
只有當所有coefficient都是real的情況才只有上述3個case.
2007-05-12 10:55 pm
d=(a+b)^2-4(1)(ab)
=a^2+2ab+b^2-4ab
=a^2-2ab+b^2
=(a-b)^2
參考: me


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