How do you find the rest of the zeros given one of the zero #c=-2# and the function #f(x)=x^3+2x^2-3x-6#?

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Answer 1 · 2016-11-30T17:56:16

#f(x) = 0# for #x=-2# and #x=+-sqrt(3)#

If #x=-2# is a root, then #f(x)# must be divisible by #(x+2)#.

We can factor #f(x)# using synthetic division :

-2 | 1...... 2....-3.....-6
..............-2......0......6
.......1.......0.....-3......0

The remainder is null, so:

#f(x)=(x+2)(x^2-3)#

Then the other two zeroes are given by:

#(x^2-3) = 0#

#x=+-sqrt(3)#