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# Who invented the quadratic equation?

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Babylonian mathematicians as early as the Sumerian Ur III period (21st to 20th century B.C.) used geometric methods to solve second-degree problems. Similar geometric methods solved quadratic equations in later Babylonia, Egypt, Greece, China, and India. Indian mathematician Brahmagupta (597-668 C.E.) was the first to give an explicit solution.

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Ancient Babylonians understood second-degree equations as geometric problems of sides and areas of rectangles and squares. The equation can be geometrically stated as saying that if a rectangle with sides of the length s and f/2 * s is removed from a rectangle with sides p and s, then the remainder is a rectangle of given area B. Euclid summarized these geometric solutions in Book II of the Elements where he represented such problems by a combination of rectangles and lines.

Brahmagupta of India was instrumental in understanding that numbers are abstract concepts which can be zero or negative. He pointed out that quadratic equations can have two possible solutions, one of which can be negative. He derived algebraic solutions to quadratic equations and went several steps further by solving systems of equations and quadratic equations with two unknowns. The latter was not considered by European mathematicians until more than a millennium later.

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## Related Questions

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According to Dictionary.com, the word "quadratic" is derived from the Latin word "quadratus" and means "square." In math, a quadratic refers to a polynomial where the highest degree of the term is two, which means the largest term in the polynomial is squared or raised to the second power.

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To find the vertex of a quadratic equation, determine the coefficients of the equation, then use the vertex x-coordinate formula to find the value of x at the vertex. Once the x-coordinate is found, plug it into the original equation to find the y-coordinate.

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To solve the quadratic equation ax^2 + bx + c - 0, plug the corresponding numbers into the quadratic formula. Take the opposite of b, and provide the option of adding or subtracting the square root of (b^2 - 4ac). Divide the result by 2a.