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Solutions to a Quadratic Inequality

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Find the range and graph of the solutions to the quadratic inequality.
Quadratic Inequality
\(\\ \hspace{30px} ax^2+bx+c\ \left\{\begin{array}{1}{\large{\gt0}\\ {\ge0}\\ {\lt0}\\ {\le0}} \end{array}\right.\)
Inequality: ax2+bx+c
 
a
(a≠0)
b
c
Roots of the quadratic equation ax2+bx+c=0

\(\normalsize\\ (1)\ roots:\hspace{30px} \alpha={\large\frac{-b+\sqrt{b^2-4ac}}{2a}}\\ \hspace{100px} \beta={\large\frac{-b-\sqrt{b^2-4ac}}{2a}} \\ (2)\ double\ root:\ \alpha={\large\frac{-b}{2a}}\ , if\ b^2-4ac=0\\\)

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