已知关于x的方程x^2+px+q=0的两实根为tanθ和tan(π/4+θ),且tanθ:tan(π/4+θ)=2:15,求实数p,q的值.thank you.
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tanθ:tan(π/4+θ)=tanθ:(1+tanθ)/(1-tanθ)=2:15
所以tanθ=1/5或tanθ=2/3 则对应的tan(π/4+θ)=3/2或tan(π/4+θ)=5
所以p=-(tanθ+tan(π/4+θ))=-(1/5+3/2)=-17/10
q=tanθ*tan(π/4+θ)=1/5*3/2=3/10
或者p=-(tanθ+tan(π/4+θ))=-(2/3+5)=-17/3
q=tanθ*tan(π/4+θ)=2/3*5=10/3