The function f (x) = x ^3 + 2x^2 - 5 x - 6 has a root at 2. Name all roots of this function.

a.-2, - 1, - 3

b. 2, 1, 3

c. 2, - 1, - 3

d.-2, 1, 3

sub x=1 into f (x),

remainder = 1^3+2 (1) ^2-5 (1) - 6 = - 8

since remainder≠0, x=1 is not a root of the function

sub x=-1,

remainder = (-1) ^3+2 (-1) ^2-5 (-1) - 6 = 0

by remainder theorem,

x=-1 is a root of f (x)

hence, the correct ans is c