二次方程功課問題

2011-02-26 4:11 am
if x=3+4j is a root of x^2+ax+b=0,find the real numbers a and b
唔係用呢條equation....x= -b+ - root b^2 -4ac/2a咩....
我見到其他地方有answer不過唔明點計.......計黎計去都唔得....請問有無人話我知
x^2 + ax + b = 0

For x = 3 + 4j is a root, then its conjugate x = 3 - 4j must be another root.

Sum of roots, -a = (3 + 4j) + (3 - 4j) = 6

So, a = -6

Product of roots, b = (3 + 4j)(3 - 4j) = (3)^2 - (4j)^2 = 9 - (-16) = 25

So, a = -6, b = 25

回答 (2)

2011-02-26 6:12 am
✔ 最佳答案
x^2 + ax + b = 0
3 + 4j is one of the root
(3 + 4j)^2 + a(3 + 4j) + b = 0
9 + 24j - 16 + 3a + 4aj + b = 0
(3a + b - 7) + (24 + 4a)j = 0
So 3a + b - 7 = 0 ---(1)
24 + 4a = 0 ---(2)
For (2), a = -6
Put a = -6 into (1), 3(-6) + b - 7 = 0
b = 25

2011-02-26 12:05:34 補充:
Have you learnt complex number...
參考: Knowledge is power.
2011-02-27 10:43 am
我讀緊IVE D notes唔係講解咁多


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