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