Question

Find the rational solution of x3 – 3x2 + x + 5 = 0. Show your use of the Rational Zero Theorem to receive credit!

Answer 1

       A zero of a function is a number that, when plugged in for the variable, makes the function equal to zero.
P ( x ) = 0
As P ( - 1 ) = 0:
( x³ - 3 x² + x + 5 ) : ( x + 1 ) = x² - 4 x + 5
 -x³ -  x²
--------------
      - 4 x² + x
        4 x²+ 4 x
       --------------
                 5 x + 5
                -5 x -  5
                ------------
                          0
The remaining trinomial: x² - 4 x + 5 doesn´t have rational roots.
Answer: x = -1