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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle x^{2} - 5 x + 4=0\)
Since \(\displaystyle a=1\) we need to find factors of \(\displaystyle 4\) that add up to \(\displaystyle -5\). 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 $x^{2} - 5 x + 4=0$
\soln{9cm}{Since $a=1$ we need to find factors of $4$ that add up to $-5$. The factors are $-1$ and $-4$. This gives $(x - 1)(x - 4)=0$. The solutions are $x = 1$ and $x = 4$}
\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} - 5 x + 4=0 " src="/equation_images/%20%5Cdisplaystyle%20x%5E%7B2%7D%20-%205%20x%20%2B%204%3D0%20" alt="LaTeX: \displaystyle x^{2} - 5 x + 4=0 " data-equation-content=" \displaystyle x^{2} - 5 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%204%20" alt="LaTeX: \displaystyle 4 " data-equation-content=" \displaystyle 4 " /> that add up to <img class="equation_image" title=" \displaystyle -5 " src="/equation_images/%20%5Cdisplaystyle%20-5%20" alt="LaTeX: \displaystyle -5 " data-equation-content=" \displaystyle -5 " /> . The factors are <img class="equation_image" title=" \displaystyle -1 " src="/equation_images/%20%5Cdisplaystyle%20-1%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-%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%201%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>