# A Simple Proof of the Quadratic Formula

@article{Loh2019ASP, title={A Simple Proof of the Quadratic Formula}, author={Po-Shen Loh}, journal={arXiv: History and Overview}, year={2019} }

This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the potential to demystify quadratic equations for students worldwide.

## 9 Citations

### A Geometric Interpretation of the Quadratic Formula.

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- Computer ScienceGANIT: Journal of Bangladesh Mathematical Society
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In this expository note, the factorization of a general quadratic expression basically requires solution to a hyperbola and a line and some other methods, namely, Linear Method, Average Method and Difference of two Squares Method are discussed.

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- BusinessThe College Mathematics Journal
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Summary This article provides an intuitive, simple and computationally efficient method to solve for general quadratic equations compared to the traditional completing the square method. The only…

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The novel Moving-update Kalman algorithm, which combines MA and Kalman methods, can track data recursively without prior knowledge of noise’s variance and is of linear complexity and, hence, fast enough for low cost IoT and FWMS systems in developing countries like Vietnam.

## References

SHOWING 1-10 OF 22 REFERENCES

### Beyond the Quadratic Formula

- Mathematics
- 2013

Preface 1. Polynomials 2. Quadratic polynomials 3. Cubic polynomials 4. Complex numbers 5. Cubic polynomials, II 6. Quartic polynomials 7. Higher-degree polynomials Bibliography Index.

### The Babylonian Quadratic Equation

- PhysicsThe Mathematical Gazette
- 1956

The purpose of this note is to show at a glance the significance of successive steps in the solutions to some of the quadratic equations that have come down in the cuneiform texts as examples of the…

### Diophantus of Alexandria: a Study in the History of Greek Algebra

- Mathematics, HistoryNature
- 1911

THIS is far from being a mere reprint of the first edition; in fact, it is in great part a new work, which, in conjunction with Tannery's critical edition of the “Arithmetica,” makes Diophantus at…

### A History of Mathematics: An Introduction

- Mathematics
- 1998

Ancient mathematics the beginnings of mathematics in Greece Archimedes and Appolinius mathematics methods in Hellenistic times the final chapters of Greek mathematics medieval China and India the…

### Unknown Quantity: A Real and Imaginary History of Algebra

- History
- 2007

If you are searched for a book by John Derbyshire Unknown Quantity: A Real and Imaginary History of Algebra in pdf form, in that case you come on to the faithful site. We furnish full edition of this…

### Algebra, with arithmetic and mensuration, from the Sanscrit of Brahmegupta and Bháscara ; translated by Henry Thomas Colebrooke

- Mathematics
- 1973

Dissertation Part I. Bhascara: 1. Introductions 2. Invocation 3. Miscellaneous 4. Mixture 5. Progression 6. Plane figure 7. Excavations and contents of solids 8. Stacks 9. Saw 10. Mounds of grain 11.…