Question

X^3-6x^2 11x-6=0 a. 1,-5,4 1/3 b. 1,5,4 1/3 c. 0,-5,-4 1/3 d. 0,5,-4 1/3

Answer 1

X^3 - 6x^2 + 11x - 6 = 0
f(1) = 1^3 - 6(1)^2 + 11(1) - 6 = 1 - 6 + 11 - 6 = 0
This means that x - 1 is a factor of x^3 - 6x^2 + 11x - 6 = 0

                     x^2 - 5x + 6
                ___________________
x - 1        |     x^3 - 6x^2 + 11x - 6
             - |     x^3 - x^2
               |______________     
               |          -5x^2 + 11x - 6  
             - |          -5x^2 + 5x
               |_____________________
               |                        6x - 6
             - |                        6x - 6

x^3 - 6x^2 + 11x - 6 = (x - 1)(x^2 - 5x + 6) = (x - 1)(x - 2)(x - 3)
Therefore, solutions to x^3 - 6x^2 + 11x - 6 are 1, 2 and 3.