Solve for x: `2x^4+x^3-11x^2+x+2=0`

Explanation

Since `x=0`s is not a solution of the give equation.
On dividing by `x^(2)` in both sides of the given equation, we get
`2(x^(2)+1/(x^(2)))+(x+1/x)-11=0`……..i
Put `x+1/x=y` in Eq. (i) then Eq. (i) reduce in the form
`2(y^(2)-2)+y=11=0`
`implies2y^(2)+y-15=0`
`:.y_(1)=-3` and `y_(2)=5/2`
Consequently the original equation is equivalent to the collection of equations.
`{(x+1/x=-3),(x+1/x=5/2):}`
we find that `x_(1)=(-3-sqrt(5))/2,x_(2)=(-3+sqrt(5))/2,x_(3)=1/2,x_(4)=2`