SOLUTION: Solve The following equation that has 3 roots(solutions): x^3 - 3x^2 - 4x + 12 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Solve The following equation that has 3 roots(solutions): x^3 - 3x^2 - 4x + 12 = 0      Log On


   



Question 205129: Solve The following equation that has 3 roots(solutions):
x^3 - 3x^2 - 4x + 12 = 0

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

Solve The following equation that has 3 roots(solutions):

x%5E3+-+3x%5E2+-+4x+%2B+12+=+0

Factor x%5E2 out of the first two terms 
on the left only:

x%5E2%28x+-+3%29+-+4x+%2B+12+=+0

Factor -4 out of the last two terms 
on the left:

x%5E2%28x+-+3%29+-+4%28x+-+3%29+=+0
 
Factor %28x-3%29 out of the left side:

%28x+-+3%29%28x%5E2+-+4%29+=+0

Factor what's in the second parentheses
as the difference of squares:

%28x+-+3%29%28x-2%29%28x%2B2%29+=+0

Set each factor equal to 0

x-3=0 gives solution x=3

x-2=0 gives solution x=2

x%2B2=0 gives solution x=-2

Edwin