Differential Equations For Dummies
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A quadratic equation is any second-degree polynomial equation — that’s when the highest power of x, or whatever other variable is used, is 2. The solution or solutions of a quadratic equation,


Solve the equation,


with the quadratic formula:

  1. Bring all terms to one side of the equation, leaving a zero on the other side.

  2. Plug the coefficients into the formula.

    In this example, a equals 2, b is –5, and c is –12, so


You can also use the quadratic formula for factoring trinomials.


Here’s what you do.

  1. Use the quadratic formula to get solutions for x. (You can also use your calculator to get the solutions.) Make sure the solutions are written as fractions rather than as decimals and that they’re reduced to lowest terms.

  2. Take the two solutions and put them in factors. If a solution is positive, use subtraction. If a solution is negative, use addition.

  3. If either solution is a fraction, take the denominator and bring it in front of the x.


    And, voilà, the trinomial is factored:

    (x – 4)(2x + 3)

About This Article

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About the book author:

Steven Holzner was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.

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