Hello, Sean!
Krizalid is absolutely correct . . .
Find the set of values for which the graph of $\displaystyle y\:=\:2x^2+x10$ is above the xaxis.
Well, that gives us the inequality: .$\displaystyle 2x^{2}+x10\:>\:0\quad\Rightarrow\quad(2x+5)(x2)>0$ . Right!
If the product of those two factors is positive:
. . (1) both factors are positive, or
. . (2) both factors are negative.
Case (1): .$\displaystyle \begin{array}{ccccccc}2x+5 & > & 0 & \Rightarrow & x & > & \text{}\frac{5}{2} \\
x  2 & > & 0 & \Rightarrow & x & > & 2\end{array}$ . The "stronger" inequality is: .$\displaystyle x \:>\:2$
Case (2): .$\displaystyle \begin{array}{ccccccc}2x + 5 & < & 0 & \Rightarrow & x & < &\text{}\frac{5}{2} \\
x  2 & < & 0 & \Rightarrow & x & < & 2\end{array}$ . The "stronger" inequality is: .$\displaystyle x \:<\:\text{}\frac{5}{2}$
Therefore, the graph is above the xaxis on the intervals: .$\displaystyle \left(\text{}\infty,\,\text{}\frac{5}{2}\right),\;(2,\,\infty)$
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Of course, if we were allowed to graph the function,
. . we could have "eyeballed" the answers. Code:

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