4

cubic equation:

$$ax^3+bx^2+cx+d=0$$

Cube means 3.

Quadratic equation:

$$ax^2+bx+c=0$$

Quad means 4. But it is a power of two, should it be called bi... Equation.

My question is: Is this a mistake in naming the quadratic equation?

Qmechanic
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Doctor
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1 Answers1

24

A fourth degree polynomial is called a quartic polynomial.

Quadratic is derived from the Latin word quadratus, the past participle of quadrare, an infinitive meaning to make square.

Saketh Malyala
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  • Oh very interesting thank you for the answer – Doctor Jun 16 '17 at 09:01
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    This means that the "four" from "quad" in "quadratic" refers to the four sides of a square, not to the fourth power. Interesting. – Bob Krueger Jun 16 '17 at 13:33
  • maybe quartic, from quart? @Bob1123 – Saketh Malyala Jun 16 '17 at 13:37
  • "Quartic" is derived from the latin word "quattuor" meaning four. The English word quart is named so because a quart is four cups. It should be noted that when the degree of a polynomial is greater than 3, the polynomial is referred to with a latin-derived name. Zeroth, first, second, and third degree polynomials are the exception (constant, linear, quadratic, and cubic, resp.). – Bob Krueger Jun 16 '17 at 13:54
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    I thought a pint was four cups. No wonder I failed my life skills test @Bob1123 – Saketh Malyala Jun 16 '17 at 13:56
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    @Bob1123 No, a quart is from the Latin "quartus" (quarter) and is so called because it's a quarter-gallon. (See, e.g., the OED but any dictionary should give this etymology.) The use of the word "cup" to mean a quarter of a quart is much more recent: the earliest citation in the OED is from 1857, whereas "quart" goes back to the 14th Century. – David Richerby Jun 16 '17 at 15:32
  • @Bob1123 . The English (and Canadian) gallon is 160 ounces and the American gallon is 128 ounces. The English (and Canadian) quart is 40 ounces and the American quart is 32 ounces. At least they have the same ounce. – DanielWainfleet Jun 16 '17 at 17:15
  • @DavidRicherby thanks for the correction. I knew my Latin education wasn't great but now I'll be sure to really check these things. – Bob Krueger Jun 16 '17 at 17:23
  • @DanielWainfleet "At least they have the same ounce." Nope. An Imperial fluid ounce is 28.4ml and an American fluid ounce is 29.6ml: roughly a 5% difference. Oh, and food labels in the US use a 30ml fluid ounce. – David Richerby Jun 16 '17 at 17:49
  • @DavidRicherby........!!! I didn't know that. – DanielWainfleet Jun 16 '17 at 18:03