Question

what are all of the possible rational roots for x to the third power- x squared-x +8=0?

Answer 1

x^3 - x^2 - x + 8 = 0

tough one
- it does not factor
tried x = ±1, ±2, ±4 , none worked
so no rational root

what about real roots?

let f(x) = x^3 - x^2 - x + 8
for f(-1) = -1 -1 +1 +8 = 7
for f(-2) = -8 - 4 + 2 + 8 = -2
so there is a real root between -2 and -1
nibbling away using my calculator, if found a root at
appr x = -1.86
f(-1.86) = -.034.. , close enough