+389 Let p(x)=x^3-5x^2+12x-19 have roots a, b, and c. Find the value of 1/(ab)+1/(bc)+1/(ca).
+118608 Hi Dabae,
Let p(x)=1x^3-5x^2+12x-19 have roots a, b, and c. Find the value of 1/(ab)+1/(bc)+1/(ca).
\(a+b+c=--5/1=+5\\ ab+ac+bc=+12/1=+12\\ abc=--19/1=+19\\~\\ \frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}=\frac{c}{abc}+\frac{a}{abc}+\frac{b}{abc}=\frac{a+b+c}{abc}=\frac{5}{19}\)
+118608 Hi Dabae,
Let p(x)=1x^3-5x^2+12x-19 have roots a, b, and c. Find the value of 1/(ab)+1/(bc)+1/(ca).
\(a+b+c=--5/1=+5\\ ab+ac+bc=+12/1=+12\\ abc=--19/1=+19\\~\\ \frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}=\frac{c}{abc}+\frac{a}{abc}+\frac{b}{abc}=\frac{a+b+c}{abc}=\frac{5}{19}\)
