Answer:
The rational roots of the equation are:
x= -1.10355
x= 0.148953
x= 0.706883
x= -1
Step-by-step explanation:
We have to find the rational solutions of the algebraic equation:
[tex]x^8-4x^5+13x^3-7x+1=0.[/tex]
This equation could also be written as:
[tex](x+1)(x^7-x^6+x^5-5x^4+5x^3+8x^2-8x+1)=0[/tex]
for finding the roots of the equation we have to find the possible values of x.
Clearly the equation has 8 roots as the degree of the equation is 8.
from the graph of the following function we could see that the rational roots of the function are:
x= -1.10355
x= 0.148953
x= 0.706883
x= -1
The rest 4 roots of the equation are the complex roots.
