How to Check the Answers in Quadratic Equations

A quadratic equation is an algebraic representation of a parabola.
••• Comstock/Comstock/Getty Images

A quadratic equation can have one, two or no real solutions. The solutions, or answers, are actually the roots of the equation, which are the points where the parabola that the equation represents crosses the x-axis. Solving a quadratic equation for its roots can be complicated, and there is more than one method to do it, including completing the square, basic factoring and the quadratic formula. Whatever method you use, test the roots to confirm that they are correct. Check your answers to a quadratic equation by reworking them into the original equation and seeing if they equal 0.

    Write the quadratic equation and the roots that you calculated. For example, let the equation be x² + 3x + 2 = 0, and the roots be -1 and -2.

    Substitute the first root into equation and solve. For this example, substituting -1 into x² + 3x + 2 = 0 results in (-1)² + 3(-1) + 2 = 0, which becomes 1 - 3 + 2 = 0, which is 0 = 0. The first root, or answer, is correct, since you get 0 when you replace the variable "x" with -1.

    Substitute the second root into the equation and solve. Substituting -2 into x² + 3x + 2 = 0 results in (-2)² + 3(-2) + 2 = 0, which becomes 4 - 6 + 2 = 0, which is 0 = 0. The second root, or answer, is also correct, since you get 0 when you replace the variable "x" with -2.

Related Articles

Montessori-Inspired Toys & Kits for Your Little Scientist
How to Find the Roots of a Quadratic
How to Get Rid of Cubed Power
How to Find Cube Root in Ti-84
How to Factor & Simplify Radical Expressions
How to Solve Cubic Equations
How to Find the Square of Binomial
How to Factorise a Quadratic Expression
What Is the Definition of a Common Solution in College...
How to Find the Roots of a Polynomial
How to Factor Perfect Square Trinomials
How to Break Apart Numbers You Are Subtracting
How to Solve Cubic Polynomials
Facts About the Root Cells of Plants
When Solving Quadratic Equations, What Questions Should...
How to Get Rid of Exponents in an Algebraic Equation
How to Calculate Correlation
How to Solve Linear Systems Algebraically
How to Calculate Exponents
How to Write Quadratic Equations Given a Vertex & Point
How to Factor Polynomials With 4 Terms