we are given
[tex]f(x)=2x^4-x^3+x-2[/tex]
we can check each options
option-A:
-1,1
we can plug x=-1 and x=1 and check whethet f(x)=0
At x=-1:
[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]
[tex]f(-1)=0[/tex]
At x=1:
[tex]f(1)=2(1)^4-(1)^3+(1)-2[/tex]
[tex]f(1)=0[/tex]
so, this is TRUE
option-B:
0,1
we can plug x=0 and x=1 and check whethet f(x)=0
At x=0:
[tex]f(0)=2(0)^4-(0)^3+(0)-2[/tex]
[tex]f(0)=-2[/tex]
At x=1:
[tex]f(1)=2(1)^4-(1)^3+(1)-2[/tex]
[tex]f(1)=0[/tex]
so, this is FALSE
option-C:
-2,-1
we can plug x=-2 and x=-1 and check whethet f(x)=0
At x=-2:
[tex]f(-2)=2(-2)^4-(-2)^3+(-2)-2[/tex]
[tex]f(-2)=36[/tex]
At x=-1:
[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]
[tex]f(-1)=0[/tex]
so, this is FALSE
option-D:
-1,0
we can plug x=-1 and x=0 and check whethet f(x)=0
At x=-1:
[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]
[tex]f(-1)=0[/tex]
At x=0:
[tex]f(0)=2(0)^4-(0)^3+(0)-2[/tex]
[tex]f(0)=-2[/tex]
so, this is FALSE
