x^5+x-10=0

There is only one sign change then there is only one real root

f(1)<0,f(2)>0 then the real root lies between 1 and 2

here Let rational number gives zero's of nth degree polynomial f(x) =a0+a1x+a2x^2+....+anx^n of integer coefficients

If p/q is rational zero of f(x), being p and q relatively prime integers, qnot equals 0then none of these integers is a zero of f(x).

then root is irrational