SOLUTION: 1. 1. Solve the quadratic equation x^2 − 2x − 3 = 0. 2. Factor 3x^3 − 12x 3. Rationalize 5/3\sqrt{x}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 1. 1. Solve the quadratic equation x^2 − 2x − 3 = 0. 2. Factor 3x^3 − 12x 3. Rationalize 5/3\sqrt{x}      Log On


   

Question 1173127: 1. 1. Solve the quadratic equation
x^2 − 2x − 3 = 0.
2. Factor 3x^3 − 12x
3. Rationalize 5/3\sqrt{x}
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
factor into (x-3)(x+1)=0
x=3, -1
-
factor out the common factors 3 and x
3x(x^2-4). Now there is a difference of squares, which may be factored
3x(x+2(x-2)
-
The last isn't clear.
(5/3)/sqrt(x)? If that is it multiply top and bottom by sqrt (x) for (5/3) sqrt(x)/x
If it is 5/(3 sqrt(x)), multiply top and bottom by sqrt(x) to get 5sqrt(x)/3x


Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.

(1)  Solve by factoring


         x^2 - 2x - 3 = 0

         (x-3)*(x+1) = 0

         The roots are  x= 3  and  x= -1.



(2)  Take factor (3x) out


         3x^3 - 12x = 3x(x^2 - 4) = 3x*(x-2)*(x+2)