Find the number of real solutions to the equation $ x^7=x+1$. The equation $x^7 = x+1 $ has:

a) no real solution
b)  no positive real solution
c) a real solution in the interval (0,2)
d) a real solution but not within (0,2)
Which is the correct answer and why ? How do i find the answer to such questions? 

Use Descartes' Rule of Signs on $f(x)=x^7-x-1$:
It states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or is less than it by an even number.
So we have one positive root. Now evaluate $f(x)$ at $0$ and $2$ to judge whether the root lies inside or outside of this interval...
