SOLUTION: find all the solutions to the equation -2x^3 -3x^2 +5x+6=0 The answer given is -2.0, -1.0, 1.5 but I do not understand how they found those solutions

Algebra ->  Rational-functions -> SOLUTION: find all the solutions to the equation -2x^3 -3x^2 +5x+6=0 The answer given is -2.0, -1.0, 1.5 but I do not understand how they found those solutions      Log On


   

Question 852954: find all the solutions to the equation -2x^3 -3x^2 +5x+6=0
The answer given is -2.0, -1.0, 1.5 but I do not understand how they found those solutions
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

-2x^3 -3x^2 +5x+6=0     |Find one root by trial and error: x = 1 NO, x = -1 YES!!

Using that root to find others with Synthetic Division:

+highlight_green%28-1%29	-2	-3	5	6

				

		2	1	-6

	-2	-1	6	0

%28-2x%5E3+-3x%5E2+%2B5x%2B6%29%2F%28x%2B1%29 = (-2x^2 -x + 6) = 0   

 (-2x^2 -x + 6) = 0    Factor

 (-2x +3)(x +2)= 0 

 (-2x +3)= 0,  x = 3/2

   (x +2)= 0,  x = -2

Roots:  x = -2, -1, 1.5