Solving Polynomial Inequalities Analytically

Exercise 4.

Find the solutions of the inequality

\begin{displaymath}x^2+5x\geq 3.\end{displaymath}


By using the quadratic formula, we find that the equation x2+5x-3=0 has as its roots


Note that




The solutions are all points in the set

\begin{displaymath}(-\infty, -\frac{5+\sqrt{37}}{2})\cup (-\frac{5-\sqrt{37}}{2},\infty).\end{displaymath}

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