# What are the possible rational roots of #x^3-4x^2+x+2=0# and then determine the rational roots?

##### 1 Answer

Apr 2, 2017

"Possible" rational roots:

Rational root:

Irrational roots:

#### Explanation:

Given:

#x^3-4x^2+x+2 = 0#

By the rational roots theorem, any rational roots of this cubic are expressible in the form

That means that the only possible rational roots are:

#+-1# ,#+-2#

In addition, notice that the sum of the coefficients is zero. That is:

#1-4+1+2 = 0#

Hence we can tell that

#0 = x^3-4x^2+x+2#

#color(white)(0) = (x-1)(x^2-3x-2)#

The remaining roots can be found using the quadratic formula.

#x = (3+-sqrt((-3)^2-4(1)(-2)))/(2*1) = 3/2+-sqrt(17)/2#