What number makes this equation true?

Answer :

We have  : $\frac{x^3 - x^2 - 4}{\left(x - 3 \right)} = 0$


At  x =   - 3 , we get

$$\begin{gathered} \frac{{\left(-3\right)}^3 - {\left(-3\right)}^2 - 4}{\left(\left(-3\right) - 3 \right)} = 0 \\ \Rightarrow \frac{-27- 9- 4}{- 6} = 0 \\ \Rightarrow \frac{-40}{- 6} \ne 0 , So \\ \mathrm{x} = - 3 \mathrm{is} \mathrm{not} \mathrm{satisfied} \mathrm{the} \mathrm{given} \mathrm{equation} . \end{gathered}$$

And

At  x = 2 , we get

$$\begin{gathered} \frac{2^3 - 2^2 - 4}{\left(2 - 3 \right)} = 0 \\ \Rightarrow \frac{8- 4- 4}{- 1} = 0 \\ \Rightarrow \frac{0}{- 1} = 0 \\ \Rightarrow 0 = 0 , So \\ \mathrm{x} = 2 \mathrm{is} \mathrm{satisfied} \mathrm{the} \mathrm{given} \mathrm{equation} . \end{gathered}$$

So, We can say at x  =  2 , This equation is true  , So

Option  (  B )                                                                                 ( Ans )