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

Question

1311 views around the world

You can reuse this answer
Creative Commons License

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:

$(x^2-3) = 0$

$x=+-sqrt(3)$

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