Question

Examine for the rational roots of

x⁸ – 3x + 1 = 0

Answer 1

Here a_n = 1, a₀ = 1

If `"p"/"q"` is a rational root of (1)

Then q is a factor a_n, p is a factor of a₀

The possible values of p and q are ± 1.

Among the possible values 1, -1, [(p, q) = 1]

None of them satisfies the equation (1)

The above equation has no rational roots