# How do you find the roots of #x^3+x^2-7x+2=0#?

##### 1 Answer

Nov 11, 2016

The roots are

#### Explanation:

Given:

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

By the rational roots theorem, any *rational* zeros of

That means that the only possible *rational* zeros are:

#+-1, +-2#

Note that:

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

So

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

We can find the zeros of the remaining quadratic factor using the quadratic formula with

#x = (-color(blue)(3) +-sqrt (color(blue)(3)^2 - 4(color(blue)(1))(color(blue)(-1))))/(2(color(blue)(1)))#

#color(white)(x) = (-3+-sqrt(9+4))/2#

#color(white)(x) = -3/2+-sqrt(13)/2#