\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Solve \(\displaystyle x^{2} - 3 x - 4=0\)
Since \(\displaystyle a=1\) we need to find factors of \(\displaystyle -4\) that add up to \(\displaystyle -3\). The factors are \(\displaystyle 1\) and \(\displaystyle -4\). This gives \(\displaystyle (x + 1)(x - 4)=0\). The solutions are \(\displaystyle x = -1\) and \(\displaystyle x = 4\)
\begin{question}Solve $x^{2} - 3 x - 4=0$
\soln{9cm}{Since $a=1$ we need to find factors of $-4$ that add up to $-3$. The factors are $1$ and $-4$. This gives $(x + 1)(x - 4)=0$. The solutions are $x = -1$ and $x = 4$}
\end{question}
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}
\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}
\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}
\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue
\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Solve <img class="equation_image" title=" \displaystyle x^{2} - 3 x - 4=0 " src="/equation_images/%20%5Cdisplaystyle%20x%5E%7B2%7D%20-%203%20x%20-%204%3D0%20" alt="LaTeX: \displaystyle x^{2} - 3 x - 4=0 " data-equation-content=" \displaystyle x^{2} - 3 x - 4=0 " /> </p> </p><p> <p>Since <img class="equation_image" title=" \displaystyle a=1 " src="/equation_images/%20%5Cdisplaystyle%20a%3D1%20" alt="LaTeX: \displaystyle a=1 " data-equation-content=" \displaystyle a=1 " /> we need to find factors of <img class="equation_image" title=" \displaystyle -4 " src="/equation_images/%20%5Cdisplaystyle%20-4%20" alt="LaTeX: \displaystyle -4 " data-equation-content=" \displaystyle -4 " /> that add up to <img class="equation_image" title=" \displaystyle -3 " src="/equation_images/%20%5Cdisplaystyle%20-3%20" alt="LaTeX: \displaystyle -3 " data-equation-content=" \displaystyle -3 " /> . The factors are <img class="equation_image" title=" \displaystyle 1 " src="/equation_images/%20%5Cdisplaystyle%201%20" alt="LaTeX: \displaystyle 1 " data-equation-content=" \displaystyle 1 " /> and <img class="equation_image" title=" \displaystyle -4 " src="/equation_images/%20%5Cdisplaystyle%20-4%20" alt="LaTeX: \displaystyle -4 " data-equation-content=" \displaystyle -4 " /> . This gives <img class="equation_image" title=" \displaystyle (x + 1)(x - 4)=0 " src="/equation_images/%20%5Cdisplaystyle%20%28x%20%2B%201%29%28x%20-%204%29%3D0%20" alt="LaTeX: \displaystyle (x + 1)(x - 4)=0 " data-equation-content=" \displaystyle (x + 1)(x - 4)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = -1 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-1%20" alt="LaTeX: \displaystyle x = -1 " data-equation-content=" \displaystyle x = -1 " /> and <img class="equation_image" title=" \displaystyle x = 4 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%204%20" alt="LaTeX: \displaystyle x = 4 " data-equation-content=" \displaystyle x = 4 " /> </p> </p>