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Use the discriminant, b2−4ac to determine the number and type of solutions to the equation x2−x+8=0. No points will be given if the discriminant is not used.

Since the discriminant is b2−4ac=(−1)2−4(1)(8)=−31 and is negative, the equation has two imaginary solutions.

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\begin{question}Use the discriminant, $b^2-4ac$ to determine the number and type of solutions to the equation $x^{2} - x + 8 = 0$.  No points will be given if the discriminant is not used.
    \soln{9cm}{Since the discriminant is $b^2-4ac=(-1)^2-4(1)(8)=-31$ and is negative, the equation has two imaginary solutions.}

\end{question}

Download Question and Solution EnvironmentLATEX
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\usepackage{tcolorbox}

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\ShowSolutiontrue

\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

\end{question}\end{document}
HTML for Canvas 
<p> <p>Use the discriminant,  <img class="equation_image" title=" \displaystyle b^2-4ac " src="/equation_images/%20%5Cdisplaystyle%20b%5E2-4ac%20" alt="LaTeX:  \displaystyle b^2-4ac " data-equation-content=" \displaystyle b^2-4ac " />  to determine the number and type of solutions to the equation  <img class="equation_image" title=" \displaystyle x^{2} - x + 8 = 0 " src="/equation_images/%20%5Cdisplaystyle%20x%5E%7B2%7D%20-%20x%20%2B%208%20%3D%200%20" alt="LaTeX:  \displaystyle x^{2} - x + 8 = 0 " data-equation-content=" \displaystyle x^{2} - x + 8 = 0 " /> .  No points will be given if the discriminant is not used.</p> </p>
HTML for Canvas
<p> <p>Since the discriminant is  <img class="equation_image" title=" \displaystyle b^2-4ac=(-1)^2-4(1)(8)=-31 " src="/equation_images/%20%5Cdisplaystyle%20b%5E2-4ac%3D%28-1%29%5E2-4%281%29%288%29%3D-31%20" alt="LaTeX:  \displaystyle b^2-4ac=(-1)^2-4(1)(8)=-31 " data-equation-content=" \displaystyle b^2-4ac=(-1)^2-4(1)(8)=-31 " />  and is negative, the equation has two imaginary solutions.</p> </p>