Question

Show that x^4 + x^3 − 4x + 1 = 0 has a root in (0,1)

Answer 1

Given, the equation x⁴ + x³ − 4x + 1 = 0.

Since, f(0).f(1)=1.(1+1-4+1)=-1<0.

Therefore, by Bolzano theorem the given equation has a zero in (0,1).