Remember that
If a root is substituted in the given polynomial, then, the value of the polynomial must be zero
so
we have
x^4 - 2x^3 - 7x^2 -8x +12
Verify
For x=2
(2^4)-2(2)^3-7(2^2)-8(2)+12
16-16-28-16+12
-34+12
-22 ------> is not equal to zero
that means ------> the value of x=2 is not a root
Verify For x=-1
(-1)^4-2(-1)^3-7(-1)^2-8(-1)+12
1+2+7+8+12
30 ----> is not equal to zero
that means ------> the value of x=-1 is not a root
Verify for x=3
(3)^4-2(3)^3-7(3)^2-8(3)+12
81-54-63-24+12
-48 ---> is not equal to zero
that means ------> the value of x=3 is not a root
Verify for x=-2
(-2^4)-2(-2)^3-7(-2^2)-8(-2)+12
16+16-28+16+12
32 -> is not equal to zero
that means ------> the value of x=-2 is not a root