\chapter{Polynomial and rational functions}
\section{Quadratic inequalities}
Answer the questions in your own words.
\begin{enumerate}
\item
When writing the solution of the quadratic inequality \((x-1)(x+4)\geq 0\) in
interval notation, the numbers
1 and \(-4\) will appear in the solution. Do we need to use
parentheses or brackets around them?
\item
When writing the solution of the quadratic inequality \(-(x+5)^2 < 0\) in
interval notation, the number \(-5\) will appear in the solution.
Do we need to use
parentheses or brackets around it?
\item
What are the steps to solve the quadratic inequality \(a(x-3)(x+6)\leq 0\)?
\item
What are the steps to solve the quadratic inequality \(a(x-2)(x+2) > 0\)?
\item
Suppose that when we solve the quadratic equation \(2x^2 +bx +c=0\) we find no solutions.
What is the solution of the quadratic inequality \(2x^2+bx+c> 0\)?
\item
Suppose that \(f(x)\) is a quadratic function with \(x=2\) and \(x=5\) as zeros.
When we solve the inequality
\(f(x)\geq 0\), could \((-\infty,2)\cup (5,\infty)\) be the solution?
\item
Suppose that \(f(x)\) is a quadratic function. What inequality do we need to solve to
find the domain of \(\sqrt{f(x)}\)?
\item
Suppose that \(f(x)\) is a quadratic function. What inequality do we need to solve to
find the domain of \(\displaystyle \frac{1}{\sqrt{f(x)}}\)?
\item
A quadratic function \(f(x)\) has no zeros, and \(f(0)=1\). What is the domain of
\(\displaystyle \frac{1}{\sqrt{f(x)}}\)?
\end{enumerate}