What are the real roots of equation x^3 + x - 1 ?
I tried to factor the equation but it doesn't help me here. I noticed that f(0) = -1 and f(1) = 1. So there must exist at least one real root in-between 0 and 1 but I am not able to find it.
Can someone please help me ?
While definitely not the most efficient method for finding the root(s) of a given cubic equation, there is a general formula you can use to solve $ax^3+bx^2+cx+d=0$
$x = (q+(q^2+(r-p^2)^3)^{1/2})^{1/3}+(q-(q^2+(r-p^2)^3)^{1/2})^{1/3}+p$
where
$p = \frac{-b}{3a}$,
$q = p^3+\frac{bc-3ad}{6a^2}$, and
$r = \frac{c}{3a}$
With this, you should be able to find the exact form of the unique real solution to $x^3+x - 1 = 0$