Question

State the following statement is True or False

The root of the equation $x^3-2x-5=0$ lie in the interval $(2,3)$.

• A. True
• B. False

Answer 1

The correct option is A True

When a root of an equation lies in the interval $(a,b)$, $f\left(a\right)\times f\left(b\right)<0$

Here, $f\left(x\right)=x^3-2x-5$

$f\left(2\right)=2^3-2\times 2-5=8-4-5=-1$

$f\left(3\right)=3^3-2\times 3-5=27-6-5=16$

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