已知 tanθ和tan(4⼀π-θ)是方程x눀+px+q=0的两个根,且有tanθ:tan(4⼀π-θ)=3:2,求p与q的值。

2024-12-02 11:22:32
推荐回答(1个)
回答1:

根据韦达定理有:
tanθ+tan(π/4-θ)=-p (1)
tanθ*tan(π/4-θ)=q (2)
tanθ:tan(π/4-θ)=3:2
2tanθ=3(1-tanθ)/颤洞(1+tanθ)
2tan²θ+5tanθ-3=0
tanθ=1/2 或 tanθ=-3
tan(π/4-θ)=(1-tanθ)/(1+tanθ)
tan(π/4-θ)=(1-1/2)/(1+1/2)=1/3
tan(π/4-θ)=(1+3)/(1-3)=-2
代燃陆入茄段枯(1) (2)得:
p=-(1/2+1/3)=-5/6, q=1/2 * 1/3=1/6

p=-(-3-2)=5, q=-3*(-2)=6