Think about both situations and each step you take to solve them.
See solution.
Practice makes perfect
Solving a quadratic inequality implies solving the corresponding quadratic equation, so the processes are similar. We will use a table to compare them and the similarities and differences between them.
Quadratic Equation
Quadratic Inequality
We can use factoring, graphing, completing the square or the Quadratic Formula to find the solutions.
We can use factoring, graphing, completing the square or the Quadratic Formula to find the boundaries.
If the discriminant is negative there are no real solutions.
If the discriminant is negative the solution set will be either all real numbers or the empty set.
Once we have solved the equation the problem is finished.
After finding the boundaries we still need to test a point inside each of the intervals that the boundaries define to see which of them are part of the solution set.
