Calculus 8th Edition

See sec.1-8, Intermediate Value Theorem. If f is continuous on [a,b], N amy number between f(a) and f(b), f(a) $\neq$ f(b).Then, there exists a c in [a,b] such that f(c)=N. ------------- $f(x)=x^{10}-10x^{2}+5$ is a polynomial, so it is continuous everywhere. $f(0)=5 > 0$ $f(2)=1024-400+5 > 0 ,$ which does not help, as we can not apply the Intermediate Value Theorem for [0,2]. But, $f(1)=1-10+5 < 0$, so, there will be a c in $[0,1]$ such that $f(c)=0.$ $c\neq 0, \ \ c\neq 1$ and $\ \ c\in(0,2)$, So, the statement is true.