We need to find where x =0 on the given equation:
[tex]6x^3+13x^2-10x-24[/tex]Now, we need to use the given solutions to find where the expression is equal to zero.
For x=1
[tex]6(1)^3+13(1)^2-10(1)-24=6+13-10-24[/tex][tex]=-15[/tex]For x=2
[tex]6(2)^3+13(2)^2-10(2)-24=48+52-20-24[/tex][tex]=56[/tex]For x=3
[tex]6(3)^3+13(3)^2-10(3)-24=162+108-30-24[/tex][tex]=225[/tex]For x=-2
[tex]6(-2)^3+13(-2)^2-10(-2)-24=-48+52+20-24[/tex][tex]=0[/tex]Therefore, the correct solution for x is -2.