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How to factorise r^4+r^2+1 ? |
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Answer» take r^2 =tthen we can get simple quadratic eq. t^2 +t +1=0t={-1+(1-4)^0.5}/2,{-1-(1-4)^0.5)}/2t=-1/2 +sqrt(3) i /2,-1/2-sqrt(3) i /2r=t^0.5r={-1/2+sqrt(3) i /2}^0.5, {-1/2-sqrt(3) i/2}^0.5 ans is this r^4 +r^2 +1add and subtract r^3 , r^2 and rwe get, r^4 +(r^3+r^2 -r^3 -r^2 +r -r )+r^2 +1now arranging them=(r^4 +r^3 +r^2)-(r^3 +r^2 +r)+(r^2 +r+1)=r^2(r^2+r+1)-r (r^2 +r+1)+1 (r^2 +r+1)=(r^2-r+1)(r^2 +r+1) is there any trick to factorise the polynomial ? some times tricks are not applied to all questions so we have try hit and trial method. |
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