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3 years ago

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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

1 answer:

Ksju [112]3 years ago

4 0

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.

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