# How do you find all the zeros of #x^3+2x^2-2x-3#?

##### 1 Answer

Use the rational root theorem to help find the first zero

#x = (-1+-sqrt(13))/2#

#### Explanation:

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

By the rational root theorem, any rational zeros of

That means that the only possible rational zeros are:

#+-1# ,#+-3#

Trying each in turn, we find:

#f(1) = 1+2-2-3 = -2#

#f(-1) = -1+2+2-3 = 0#

So

#x^3+2x^2-2x-3 = (x+1)(x^2+x-3)#

The remaining quadratic factor is of the form

#x = (-b+-sqrt(b^2-4ac))/(2a)#

#=(-1+-sqrt(1-(4*1*-3)))/(2*1)#

#=(-1+-sqrt(13))/2#