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#