How do you find all zeros of #F(x)= x^3 -8x^2 +25x -26#?
1 Answer
There are three solutions:
Explanation:
The rational root theorem tells us that rational roots to a polynomial equation with integer coefficients can be written in the form
The polynomial equation is
The integer factors of the constant
The integer factors of the leading coefficient
The rational solutions must therefore be among the following:
Try each answer by substituting them into
Now we know that
(Polynomial divison might need its own explanation for those who haven't learned it. If there's a separate Socratic thread on it, it should be linked here.)
With the factorized polynomial
A quadratic equation
Plug
Now we have found all three solutions: