Question

find roots:
x^4+2x^3+3x^2+2x+1=0

Answer 1

First of all divide the whole equation with x^2 to
make it quadratic equation then we will we the
roots of this equation.

Answer 2

but if ewe do it then last two terms have -ve exponents.then?

Answer 3

Ntice that
\[
x^4 + 2 x^3 + 3 x^2 + 2 x + 1 == (1 + x + x^2)^2
\]
It should be easy now to use the quadratic formula.

Answer 4

To otain the above notice that
\[
x^4+2 x^3+3 x^2+2 x+1=\\x^4+2
x^3+2 x^2+x^2+2 x+1=\\x^4+2
(x+1) x^2+(x+1)^2=\left(x^2+x+1\right)^2\\

\]