Question

Find all rational solutions of the equation x8−4x5+13x3−7x+1=0.

Answer 1

The rational roots of the equation are:

x= -1.10355

x= 0.148953

x= 0.706883

x= -1

Explanation:

We have to find the rational solutions of the algebraic equation:

`x^8-4x^5+13x^3-7x+1=0.`

This equation could also be written as:

`(x+1)(x^7-x^6+x^5-5x^4+5x^3+8x^2-8x+1)=0`

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.