Question

how to prove that x^6+x^4+x^2+x+3=0 has no positive real root???

Answer 1

\[x ^{6}+x ^{4}+x ^{2}+x+3=0\]

Answer 2

Note that \[x ^{6}+x ^{4}+x ^{2}+3=-x\]

Answer 3

If x is positive, then the left side of the equation is positive and the right side is negative. That is a contradiction since the two sides are supposed to be equal.