How come quadratic equations have three terms, when quad- means four?

Question

I never got it!

Answer 1

The "quad" in "quadratic equation" actually refers to the power of x appearing in the equation
ax^2 + bx + c
and not the number of terms. More generally the following types of equations (called polynomials) have names:
ax + b: linear
ax^2 + bx + c: quadratic
ax^3 + bx^2 + cx + d: cubic
ax^4 + bx^3 + cx^2 + dx + e: quartic
etc.

Of course this doesn't answer the question as to why a degree-two polynomial should be known as "quadratic". This presumably comes from the fact that originally, quadratic equations were thought of geometrically in terms of squares, which have four sides.

Answer 2

This isn't a quadratic equation, this is a cubic equation, which has 3 solutions, rather than 2 in a normal quadratic. The quadratic equation doesn't work here, so you would either have to factor the problem, or use the 'cubic equation' (like the quadratic equation, but a lot more complex). Fortunately, you can factor this equation pretty easily. Look at the first two terms, and factor out "x^2", you're left with: x^2 * (x - 2) + 3x - 6 = 0 Now for the next two terms, you can factor out a "3": x^2 * (x - 2) + 3 (x - 2) = 0 You're left with two terms, which have a common factor of (x-2): (x^2 + 3) * (x - 2) = 0 Possible solutions are x = 2, x = sqrt(3)i, x = -sqrt(3)i (i = sqrt(-1))

Answer 3

The "quad" comes from "quadrat" or something like that, meaning "square". It means a second-degree equation. It's the same reason as when we call the term x^2 as "x squared" instead of "x to the second". Similarly, a cubic equation means one where the highest term is to the exponent 3. However, a 4th degree equation is called a quartic equation, not a tesseractical equation.

Answer 4

Actually, quadratic means "square"; the highest exponent of the variable is a 2 (x squared).

Answer 5

Hey matahari, I'm onto you. That's verbatum what it says on Wikipedia!


This is C&Pd from the site:

Quadratic equations are called quadratic because quadratus is Latin for "square"; in the leading term the variable is squared.

Answer 6

Because the highest power is 2 which is squared. Quadratus is Latin for "square"

Answer 7

They are broken down into four terms.

x^2+2x+2=(x+1)(x+1)

Answer 8

Listen to modulo.

Answer 9

Yeah!!