How to Check the Answers in Quadratic Equations

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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.

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About the Author

Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.

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