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Questions: Algebra BusinessCalculus
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Use the discriminant, \(\displaystyle b^2-4ac\) to determine the number and type of solutions to the equation \(\displaystyle 5 x^{2} - 10 x - 7 = 0\). No points will be given if the discriminant is not used.
Since the discriminant is \(\displaystyle b^2-4ac=(-10)^2-4(5)(-7)=240\) and is positive, the equation has two real solutions.
\begin{question}Use the discriminant, $b^2-4ac$ to determine the number and type of solutions to the equation $5 x^{2} - 10 x - 7 = 0$. No points will be given if the discriminant is not used.
\soln{9cm}{Since the discriminant is $b^2-4ac=(-10)^2-4(5)(-7)=240$ and is positive, the equation has two real solutions.}
\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>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 5 x^{2} - 10 x - 7 = 0 " src="/equation_images/%20%5Cdisplaystyle%205%20x%5E%7B2%7D%20-%2010%20x%20-%207%20%3D%200%20" alt="LaTeX: \displaystyle 5 x^{2} - 10 x - 7 = 0 " data-equation-content=" \displaystyle 5 x^{2} - 10 x - 7 = 0 " /> . No points will be given if the discriminant is not used.</p> </p><p> <p>Since the discriminant is <img class="equation_image" title=" \displaystyle b^2-4ac=(-10)^2-4(5)(-7)=240 " src="/equation_images/%20%5Cdisplaystyle%20b%5E2-4ac%3D%28-10%29%5E2-4%285%29%28-7%29%3D240%20" alt="LaTeX: \displaystyle b^2-4ac=(-10)^2-4(5)(-7)=240 " data-equation-content=" \displaystyle b^2-4ac=(-10)^2-4(5)(-7)=240 " /> and is positive, the equation has two real solutions.</p> </p>