中視聶小倩線上看 , 聶小倩線上看第二集 , 聶小倩 中視 , 聶小倩電視劇 , 聶小倩

第二題我用根與係數的關係，把個別的兩個根加和乘，得到四個方程式，解得c=1;可是代進去的話方程式的解就變有虛數的根了阿，這題怎麼解呢?

Ans:

是虛根沒有錯誤!!

x^2+x+4=0

x=[-1+-√(15)*j]/2

令j=√(-1), D=√(15)*j; 則兩根為:

a=[-1+√(15)*j]/2=(-1+D)/2

b=[-1-√(15)*j]/2=(-1-D)/2

檢驗答案:

a+b=-1/2-1/2=1=c => (O)

a*b=(-1+D)/2*(-1-D)/2

=(1-D^2)/4

=(1-15j^2)/4

=(1+15)/4

=4 => (O)

-1-a=-1+(1-D)/2=(-1-D)/2=b => (O)

-1-b=-1+(1+D)/2=(-1+D)/2=a => (O)

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