![]() The left-hand side is now a perfect square: Now, we express the left-hand side as a perfect square, by introducing a new term (b/2a) 2 on both sides: ![]() To determine the roots of this equation, we proceed as follows: Proof of Quadratic FormulaĬonsider an arbitrary quadratic equation: ax 2 + bx + c = 0, a ≠ 0 This formula is also known as the Sridharacharya formula.Įxample: Let us find the roots of the same equation that was mentioned in the earlier section x 2 - 3x - 4 = 0 using the quadratic formula. Quadratic Formula: The roots of a quadratic equation ax 2 + bx + c = 0 are given by x = /2a. The positive sign and the negative sign can be alternatively used to obtain the two distinct roots of the equation. The two roots in the quadratic formula are presented as a single expression. There are certain quadratic equations that cannot be easily factorized, and here we can conveniently use this quadratic formula to find the roots in the quickest possible way. Quadratic formula is the simplest way to find the roots of a quadratic equation. Maximum and Minimum Value of Quadratic Expression Solving Quadratic Equations by Factorization Nature of Roots of the Quadratic Equation We shall learn more about the roots of a quadratic equation in the below content. These two solutions (values of x) are also called the roots of the quadratic equations and are designated as (α, β). Quadratic equations have maximum of two solutions, which can be real or complex numbers. Did you know that when a rocket is launched, its path is described by a quadratic equation? Further, a quadratic equation has numerous applications in physics, engineering, astronomy, etc. In other words, a quadratic equation is an “equation of degree 2.” There are many scenarios where a quadratic equation is used. The term "quadratic" comes from the Latin word "quadratus" meaning square, which refers to the fact that the variable x is squared in the equation. Ref: /abs/1910.06709 : A Simple Proof of the Quadratic FormulaĬorrection: We amended a sentence to say that the method has never been widely shared before and included a quote from Loh.Quadratic equations are second-degree algebraic expressions and are of the form ax 2 + bx + c = 0. Either way, Babylonian tax calculators would surely have been impressed. ![]() To speed adoption, Loh has produced a video about the method. The question now is how widely it will spread and how quickly. The derivation emerged from this process. Loh, who is a mathematics educator and popularizer of some note, discovered his approach while analyzing mathematics curricula for schoolchildren, with the goal of developing new explanations. “Perhaps the reason is because it is actually mathematically nontrivial to make the reverse implication: that always has two roots, and that those roots have sum −B and product C,” he says. So why now? Loh thinks it is related to the way the conventional approach proves that quadratic equations have two roots. None of them appear to have made this step, even though the algebra is simple and has been known for centuries. ![]() He has looked at methods developed by the ancient Babylonians, Chinese, Greeks, Indians, and Arabs as well as modern mathematicians from the Renaissance until today. Loh has searched the history of mathematics for an approach that resembles his, without success. Yet this technique is certainly not widely taught or known." Loh says he "would actually be very surprised if this approach has entirely eluded human discovery until the present day, given the 4,000 years of history on this topic, and the billions of people who have encountered the formula and its proof.
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