The correct option is C −3−√52
Given equation
2x4+x3−11x2+x+2=0
Dividing the given equation by x2, as x=0 is not the root of the equation.
2x2+x−11+1x+2x2=0⇒2(x2+1x2)+(x+1x)−11=0⇒2((x+1x)2−2)+(x+1x)−11=0⇒2(x+1x)2+(x+1x)−15=0
Assuming x+1x=t
2t2+t−15=0
⇒(t+3)(2t−5)=0⇒t=−3 or 52
Now,
x+1x=−3
⇒x2+3x+1=0⇒x=−3±√9−42=−3±√52
x+1x=52
⇒2x2−5x+2=0⇒(x−2)(2x−1)=0⇒x=2,12