Question

Find the interval in which the root of equation $x^3-2x-5=0$ lies?

Answer 1

For a function $f\left(x\right)$, when $f\left(a\right).f\left(b\right)<0$, there exists a root of $f\left(x\right)$ in the interval $(a,b)$

In this question, it can be easily seen that $f\left(0\right)=0-0-5=-5$

Also, $f\left(2\right)=8-4-5=-1$

But $f\left(3\right)=27-6-5=16$

Since $f\left(2\right).f\left(3\right)<0$, there lies a root of $f\left(x\right)$ in the interval $(2,3)$