+118677 Let t be a root of f(x)=x^3-x+2. Evaluate t^6-t^2+4t.
\( f(x)=x^3-x+2. \qquad Evaluate\quad t^6-t^2+4t.\\ \mbox{since t is a root I can use factor theorem and say ..}\\ t^3-t+2=0\\ t^3=t-2\\ (t^3)^2=(t-2)^2\\ t^6=t^2-4t+4\\ so\\~\\ t^6-t^2+4t\\=t^2-4t+4-t^2+4t\\=4 \)
I have not seen a question quite like this one before :)
+118677 Let t be a root of f(x)=x^3-x+2. Evaluate t^6-t^2+4t.
\( f(x)=x^3-x+2. \qquad Evaluate\quad t^6-t^2+4t.\\ \mbox{since t is a root I can use factor theorem and say ..}\\ t^3-t+2=0\\ t^3=t-2\\ (t^3)^2=(t-2)^2\\ t^6=t^2-4t+4\\ so\\~\\ t^6-t^2+4t\\=t^2-4t+4-t^2+4t\\=4 \)
I have not seen a question quite like this one before :)
