Quadratic Formula

The QuadraticFormula is used to solve equations like:

    a x^2 + b x + c = 0 .

It gives the possible values for x in terms of a, b, and c. You can derive it by completing the square; the result is this:

    If     a x^2 + b x + c = 0            then either

         - b + sqrt( b^2 - 4 a c )
    x = ---------------------------       or
                2 a

         - b - sqrt( b^2 - 4 a c )
    x = ---------------------------
                2 a

The quantity D = (b^2 - 4 a c) is called the discriminant of the quadratic equation, so

            - b ± sqrt(D)
       x = ---------------
                2 a

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While well-known, this solution is numerically unstable in some circumstances. There is a better solution given and explained in ReadLikeMath, which contains other useful insights and comments.

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Applications of the QuadraticFormula:

• MatrixAnalysis of BandPassFilter?s.
• Second order approximations
• Calculations of projectile trajectories under constant acceleration and negligible air resistance.
• Estimates of projectile ranges.

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CategoryMath