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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle x^{2} - x - 2=0\)
Since \(\displaystyle a=1\) we need to find factors of \(\displaystyle -2\) that add up to \(\displaystyle -1\). The factors are \(\displaystyle 1\) and \(\displaystyle -2\). This gives \(\displaystyle (x + 1)(x - 2)=0\). The solutions are \(\displaystyle x = -1\) and \(\displaystyle x = 2\)
\begin{question}Solve $x^{2} - x - 2=0$
\soln{9cm}{Since $a=1$ we need to find factors of $-2$ that add up to $-1$. The factors are $1$ and $-2$. This gives $(x + 1)(x - 2)=0$. The solutions are $x = -1$ and $x = 2$}
\end{question}
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\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} - x - 2=0 " src="/equation_images/%20%5Cdisplaystyle%20x%5E%7B2%7D%20-%20x%20-%202%3D0%20" alt="LaTeX: \displaystyle x^{2} - x - 2=0 " data-equation-content=" \displaystyle x^{2} - x - 2=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 -2 " src="/equation_images/%20%5Cdisplaystyle%20-2%20" alt="LaTeX: \displaystyle -2 " data-equation-content=" \displaystyle -2 " /> that add up to <img class="equation_image" title=" \displaystyle -1 " src="/equation_images/%20%5Cdisplaystyle%20-1%20" alt="LaTeX: \displaystyle -1 " data-equation-content=" \displaystyle -1 " /> . 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 -2 " src="/equation_images/%20%5Cdisplaystyle%20-2%20" alt="LaTeX: \displaystyle -2 " data-equation-content=" \displaystyle -2 " /> . This gives <img class="equation_image" title=" \displaystyle (x + 1)(x - 2)=0 " src="/equation_images/%20%5Cdisplaystyle%20%28x%20%2B%201%29%28x%20-%202%29%3D0%20" alt="LaTeX: \displaystyle (x + 1)(x - 2)=0 " data-equation-content=" \displaystyle (x + 1)(x - 2)=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 = 2 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%202%20" alt="LaTeX: \displaystyle x = 2 " data-equation-content=" \displaystyle x = 2 " /> </p> </p>