Solve the inequality: \( p^{2} \geq-2 p+3 \) Give your answer in interval notation. Enter DNE if there is no solution.
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Step-by-step Solution
1\end{align}\) - step8: Choose a value: \(\begin{align}&p_{1}=-4\\&p_{2}=-1\\&p_{3}=2\end{align}\) - step9: Test the chosen value: \(\begin{align}&p<-3\textrm{ }\textrm{is the solution}\\&-3
1\textrm{ }\textrm{is the solution}\end{align}\) - step10: Include the critical value: \(\begin{align}&p\leq -3\textrm{ }\textrm{is the solution}\\&p\geq 1\textrm{ }\textrm{is the solution}\end{align}\) - step11: The final solution is \(p \in \left(-\infty,-3\right]\cup \left[1,+\infty\right):\) \(p \in \left(-\infty,-3\right]\cup \left[1,+\infty\right)\) The solution to the inequality \( p^{2} \geq -2p+3 \) is \( p \in (-\infty,-3] \cup [1,+\infty) \) in interval notation.
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