So,f(0) is negative and f(1) is positive. Since f(x) is continuous, by the Intermediate value theorem there is a number c between 0 and 1 such that f(c)=0. Thus the given equation has a root.
Assuming contrary to the equation that `2x^5+7x-1=0` , has at least two roots a and b that is f(a)=0 and f(b)=0.
Thus by Rolle's theorem there is a number c between a and b such that f'(c)=0, which is impossible as,
`f'(x)=10x^4+7>0` for any point x in `(-oo,oo)`
Thus it is a contradiction to our assumption. So the equation has only one real root.