r, s, and t are roots of Ax^3+Bx^2+Cx+D=0. Express 1/r+1/s+1/t in terms of A, B, C, and D.

Question

anonymous · Answer

Viete's equation.

anonymous · Answer

i am going to make a guess that it is 
$$\frac{\frac{c}{a}}{-\frac{d}{a}}=-\frac{c}{d}$$ lets see if it is right

anonymous · Answer

$$\frac{1}{r}+\frac{1}{s}+\frac{1}{t}=\frac{rs+rt+st}{rst}$$  
looks good

anonymous · Answer

since we have$rst=-\frac{d}{a}$ and $rs+rt+st=\frac{c}{a}$ by those vieta's formulae

anonymous · Answer

Oh, you substitute the values. I see now. Thank you!

anonymous · Answer

yw

aravindg · Answer

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