How do you find the roots of #x^3-2x^2-5x+6=0#?

1 Answer
Dec 30, 2016

Answer:

#x in {+1, +3, -2}#

Explanation:

If we note that the sum of the coefficients of the terms equals zero
then it follows that #x=1# is one solution to this equation.

That is #(x-1)# is a factor of the right side.
Either using synthetic or long division we can obtain
#color(white)("XXX")(x^3-2x^2-5x+6)div(x-1)=color(green)(x^2-x-6)#

Using basic principles we can factor
#color(white)("XXX")(x^2-x-6) = (x-3)(x+2)#

So #x^3-2x^2-5x+6=0#

#rarr (x-1)(x-3)(+2)=0#

giving the solutions
#color(white)("XXX")x=+1 or x=+3 or x=-2#