Solving Quadratic Equations
Instructions
- The introductory video below explains the concepts in this section.
- This page also includes exercises that you should attempt to solve yourself. You can check your answers and watch the videos explaining how to solve the exercises.
- When you are done, you can use the graph to pick another section or use the buttons to go to the next section.
Learning Objectives
- The standard form for a quadratic equation and the possible number of solutions
- Solving quadratic equations with the difference of two squares formula
- Solving quadratic equations by factoring
- Solving quadratic equations with the quadratic formula and discussing the number of possible solutions
Concept Video(s)
Exercises
1.
- \(x=\pm 2\)
- \(x=\pm \dfrac{\sqrt{7}}{5}\)
- \(x=\pm \sqrt{3}\)
2.
- \(x=2, 3\)
- \(x=-2,-8\)
- \(x=-2,6\)
3.
\(x=-\dfrac{1}{2}, 4\)
4.
\(x=-\dfrac{3}{5}, \dfrac{9}{2}\)
5.
- \(x=\dfrac{2+\sqrt{92}}{4},\) \(x=\dfrac{2-\sqrt{92}}{4},\) Two unique real solutions
- \(x=\sqrt{3},\) One repeated real solution
6.
If we use the quadratic formula to solve it, we will get a \(-83\) inside the square root, which is not a real number. If we graph the quadratic, we see it never crosses the \(x\)-axis so it never equals \(0.\) Therefore, the equation has no real solution.