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Solving a Quadratic Equation with the Quadratic Formula
In this example, a quadratic equation is solved with two complex roots.
Review of the quadratic formula:
In this set of Math Tutorials we focus on the use of the quadratic formula to solve a quadratic equation. In order to solve any quadratic equation in standard form (shown below) use the quadratic formula.
ax2 + bx + c = 0
Before using the quadratic formula make sure that you write the quadratic equation in this form. Note that the quadratic equation is written with addition symbols. So, if you have a quadratic equation that involves subtraction, make sure that b or c terms get a negative sign in front in order to properly use the quadratic formula. One of the most common mistakes is to use the incorrect sign of the number in the quadratic formula.
The quadratic formula is written in this form.
The Quadratic Formula
Once you have written the quadratic equation in the proper form, then use the values of a, b, and c in the quadratic formula. Note that the plus or minus sign in the quadratic formula means that there are up to two solutions.
This set of Quadratic Formula Math Tuturials deals with these scenarios:
Quadratic Formula Results: Two real roots. This results in two value for x that make the quadratic equation a true statement.
Quadratic Formula Results: One real root. This results in one value for x that makes the quadratic equation a true statement.
Quadratic Formula Results: Two complex roots. This results in two complex numbers that, when substituted for x, makes the quadratic equation a true statement.
While there are other methods for solving a quadratic equation, the quadratic formula is the most dependable method. The quadratic formula will yield all the real or complex roots of a quadratic equation.
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The library of Math Tutorials is a comprehensive collection of worked-out solutions to common math problems. This overcomes a common limitation of most textbooks: the handful of worked-out examples for a given concept. We provide the full array of examples and solutions, allowing students to identify patterns among the solutions, in order to aid concept retention. We also have quizzes for many of these topics.
Our current inventory of Math Tutorials include:
- Math Tutorial: Examples Using Algebra Tiles
- Math Tutorial: Solving Equations in One Variable
- Math Tutorial: Solving Equations with Fractions
- Math Tutorial: Solving Equations with Percents
- Math Tutorial: Slope formula
- Math Tutorial: Midpoint formula
- Math Tutorial: Distance formula
- Math Tutorial: Graphing linear functions, given m and b
- Math Tutorial: Graphing absolute value functions
- Math Tutorial: Graphing linear inequalities
- Math Tutorial: Using the Point-Slope form
- Math Tutorial: Finding the equation of a line given two points
- Math Tutorial: Graphing parallel and perpendicular lines
- Math Tutorial: Solving quadratics graphically
- Math Tutorial: Solving quadratics by completing the square
- Math Tutorial: Factoring Quadratics
- Math Tutorial: Polynomial Expansion
- Math Tutorial: Solving quadratics using the quadratic formula
- Math Tutorial: Using FOIL
- Math Tutorial: Graphs of Exponential Functions
- Math Tutorial: Laws of Exponents
