The solution set of the equation x4-5x3-4x2-5x+1=0 is
3±22,-1±3i2
3±22,-1±3i
-3±22,1±3i2
3±222,1±3i
Explanation for the correct option:
Find the solution set for the given equation
Given, x4-5x3-4x2-5x+1=0
x2-5x-4-5x+1x2=0x2+1x2-5x+1x-4=0
Let, x+1x=m⇒x2+1x2=m2-2
So,
m2-5m-6=0⇒m2-6m+m-6=0⇒(m-6)(m+1)=0⇒m=6,-1
If m=6,x+1x=6
x2+1=6xx2+1-6x=0⇒x=3±22
If m=-1,x+1x=-1
x+1x=-1x2+x+1=0
Here a=1,b=1,c=1by comparing ax2+bx+c=0
x=-1±12-4(1)(1)2(1)[∵x=-b±b2-4(a)(c)2(a)]=-1±1-42=-1±-32
The discriminant b2-4ac<0 so there are two complex roots
x=-1±3i2
Hence the correct answer is option (A).