# How do you find all the zeros of #f(x)=x^3+x^2-7x+2#?

##### 1 Answer

Apr 16, 2016

#### Answer:

#### Explanation:

By the rational root theorem, any rational zeros of

That means that the only possible rational zeros are:

#+-1# ,#+-2#

We find:

#f(2) = 8+4-14+2 = 0#

So

#x^3+x^2-7x+2 = (x-2)(x^2+3x-1)#

We can factor the remaining quadratic expression by completing the square. I will multiply by

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

#=4x^2+12x-4#

#=(2x+3)^2-9-4#

#=(2x+3)^2-(sqrt(13))^2#

#=((2x+3)-sqrt(13))((2x+3)+sqrt(13))#

#=(2x+3-sqrt(13))(2x+3+sqrt(13))#

Hence