====== Question 3, Exercise 5.3 ======
Solutions of Question 3 of Exercise 5.3 of Unit 05: Polynomials. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. 

=====Question 3=====
A rectangular solid has a volume of 144 cubic units. The width is twice the height and the length is 2 units more than the width. Find the dimensions of the solid. (:!:Correction)

** Solution. **

Consider height = $x$ units \\
width = $2x$ units \\
length = $2x+2$ units \\
Volume = 144 cubic units.

By given condition 
\begin{align*}
& x(2x)(2x+2) = 144 \\
\implies & 4x^2(x+1)=144 \\
\implies & x^2(x+1)=36 \\
\implies & x^3+x^2-36=0
\end{align*}

Suppose $$p(x)=x^3+x^2-36.$$
Since 
\begin{align*}
p(3)&=3^3+3^2-36 \\
&=27+9-36 = 0
\end{align*}
This gives $x=3$ is zeros of $p(x)$. Thus

width = $2(3)$ = 6 units \\
length = $2(3)+2$ = 8 units \\
height = 3 units

Hence the dimension is 6 units by 8 units by 3 units. GOOD


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