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The word "quad" usually stands for 4 of some thing. An example would be quadruplets - 4 babies. So I am wondering why they use the word quadratic in Algebra (the Quadratic Equation) when the polynomial is only a second-degree polynomial, meaning the highest exponent is to the second power. Why is this?

2006-10-04 14:11:05 · 6 answers · asked by Anonymous in Science & Mathematics Mathematics

6 answers

Because the leading term is squared and "quadratus" is Latin for "square"

2006-10-04 14:14:40 · answer #1 · answered by Anonymous · 0 0

Given the quartic polynomial equation x^4 - 5x² + 4 = 0 Since the equation is quartic (degree 4), then naturally it has 4 solutions. This equation is a special case of the more general quartic form ax^4 + bx³ + cx² + dx + e = 0 where b = 0 and d = 0. This is special because it can be solved easily using quadratic methods. One is by substituting another variable (say z). Let z = x² Thus, z² = x^4. x^4 - 5x² + 4 = 0 Substitute z² - 5z + 4 = 0 Factor, (z - 4)(z - 1) = 0 hence, z = 4 or z = 1. We substitute back z = x² x² = 4 or x² = 1 Thus, the "4" solutions are x = 2,x = -2,x = 1 or x = -1. -------------------------------- After all, the equation can be factored as x^4 - 5x² + 4 = 0 (x² - 4)(x² - 1) = 0 (x - 2)(x + 2)(x - 1)(x + 1) = 0 So you get the 4 solutions. I hope you get it!!!!! ^_^

2016-03-18 04:57:32 · answer #2 · answered by ? 4 · 0 0

The name quadratic goes back to the time (before Descartes liberated algebra) when an algebraic expression referred to a geometric object: a second degree expression stood for an area. (Hence the terminology "square" for the second power: x2 is the number of unit squares in an x by x square). One of the problems in classical mathematics dating back to the time of Pythagoras is to find the area of a square that would exactly equal that of some figure bounded by a curve, such as a circle. This is sometimes called "effecting a quadrature" from the Latin word quadratura - the act of making square or quadratum - square. A third degree equation is similarly called a CUBIC (because of its relationship to the volume of a cube), and a fourth degree equation was looked upon with suspicion.

2006-10-04 14:14:44 · answer #3 · answered by Funkmeister 3 · 0 0

In mathematics, a quadratic equation is a polynomial equation of the second degree.
Quadratic equations are called quadratic because quadratus is Latin for "square"; in the leading term the variable is squared.

2006-10-04 14:15:14 · answer #4 · answered by kezongputi 2 · 0 0

^2 means squared, and squares are 4 sided, so its a quadratic.

think of it like this, to find the area of a square you say x^2.

2006-10-04 15:47:20 · answer #5 · answered by Sherman81 6 · 0 0

The area of a square is x^2.
I think this is what the name comes from.

2006-10-04 14:14:41 · answer #6 · answered by Anonymous · 0 0

maybe because it is set up in 4 different subequations

2006-10-04 14:15:00 · answer #7 · answered by cabjr1961 4 · 0 0

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