Question

Find all real solutions of the equation. (enter your answers as a comma-separated list. if there is no real solution, enter no real solution.) x3 − 11x2 + 24x = 0

Answer 1

Hello.  In  x3 − 11x2 + 24x = 0   please use the symbol " ^ " to denote exponentiation:

x^3 − 11x^2 + 24x = 0

First step:  factor out x:    

x^3 − 11x^2 + 24x = 0  =  x(x^2 - 11x + 24) = 0

Second step:  factor the polynomial x^2 - 11x + 24 = 0.

We can see right away that (-3)(-8) = + 24 and that 

-3
-8
---
is equal to -11.  Thus, the factors of   
x^3 − 11x^2 + 24x = 0

are x(x-3)(x-8) = 0.  The solutions are 0, 3 and 8.