Question 935701
The square parentheses mean you can INCLUDE the boundaries of the interval.


x=-2:
{{{-2(x^4-x^2-2)}}}
{{{-2((-2)^4-(-2)^2-2)}}}
{{{-2(16-4-2)}}}
{{{(neg)(pos)}}}
NEGATIVE


x=-1:
{{{-2((-1)^4-(-1)^2-2)}}}
{{{-2(1-1-2)}}}
{{{-2(-2)}}}
{{{neg*neg}}}
POSITIVE


Polynomial functions are continuous everywhere.  The function changes signs inside the given interval, so f must cross the x-axis, and therefore has a zero in the interval.