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thharrimw
- 115
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who came up with the Quadratic equation and what is the proof behind it?
Quantumduck said:The latest edition of the Mathematics Teacher, published by the NCTM has a different way to derive the quadratic formula than completing the square.
It is actually kind of elegant as well.
thharrimw said:what is it?
Ephratah7 said:what is ^?
The concept of the quadratic equation can be traced back to ancient Babylonian and Greek mathematicians, but the first known systematic solution was provided by Indian mathematician Brahmagupta in the 7th century. The modern form of the quadratic equation was developed by Persian mathematician Al-Khwarizmi in the 9th century.
The proof for the quadratic equation relies on basic algebraic principles and the use of the quadratic formula. It starts with the general form of a quadratic equation, ax^2 + bx + c = 0, and then uses the quadratic formula to solve for the roots. The proof can be found in most high school and college level algebra textbooks.
The quadratic equation is important because it is used to solve a wide range of real-world problems, from finding the maximum or minimum value of a function to predicting the trajectory of a projectile. It is also a fundamental concept in algebra and is used in higher level math courses such as calculus.
No, the quadratic equation can only be used to solve equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. Polynomial equations of higher degrees (such as cubic or quartic equations) require different methods to solve.
The quadratic equation has many practical applications in fields such as physics, engineering, economics, and statistics. It can be used to model and solve problems involving motion, optimization, and probability. Examples include calculating the maximum height of a ball thrown into the air, determining the most profitable production level for a company, and predicting the likelihood of a certain event occurring.