Does the phrase "quadratic formula" (the formula for the solutions of ax2 + bx + c = 0 [EDIT: I mean the famous formula with the square root of b2-4ac as part of the numerator]) not really get directly translated into Russian?

It seems that this is described by phrases like формула корней (или решений) квадратного уравнения or теорема Виета, but not квадратная формула.

On a related issue, I have encountered both квадратный and квадратичный, but the latter seems to be less often used (e.g., квадратичное расширение or квадратичный вычет). Is квадратичный allowed only in a more limited range of expressions, so that terms like квадратичный многочлен, квадратичный корень, or квадратичная матрица would all sound weird?

Does the phrase "quadratic formula" (the formula for the solutions of ax2 + bx + c = 0 [EDIT: I mean the famous formula with the square root of b2-4ac as part of the numerator]) not really get directly translated into Russian? It seems that this is described by phrases like формула корней (или решений) квадратного уравнения or теорема Виета, but not квадратная формула

You're right. Квадратная формула is not used in Russian. You seem to have listed the available translations yourself.

On a related issue, I have encountered both квадратный and квадратичный, but the latter seems to be less often used (e.g., квадратичное расширение or квадратичный вычет).

Квадратный is usually translated as simply `square`, квадратичный - as `quadratic`. The former term sounds less scientific than the latter, so I suppose that it's part of the reason why in some more basic expressions we use квадратный rather than perhaps the more appropriate but not established квадратичный. An example would be квадратное уравнение (if I were to establish the term anew, I'd probably go with квадратичное уравнение, but the term is already established).

Is квадратичный allowed only in a more limited range of expressions, so that terms like квадратичный многочлен, квадратичный корень, or квадратичная матрица would all sound weird?

Квадратичная матрица sounds weird because it is a square matrix (the form), not quadratic (i.e. it's not about exponent = 2). Квадратичный многочлен doesn't sound weird at all. Квадратичный корень does sound weird, because perhaps the established term квадратный корень is very widespread

• Thanks. I hadn't noticed the simple rule that квадратный=square and квадратичный=quadratic on account of the (very basic) counterexample квадратное уравнение, but once that is put aside the situation clears up! Are there any other counterexamples? For example, is квадратный многочлен an acceptable variant for квадратичный многочлен? (Note квадратный корень matches the English term square root, which is never called a quadratic root.)
– KCd
Jun 25 '12 at 17:16
• @KCd: Actually, both квадратный многочлен and квадратичный многочлен sound normal to me, although I'd probably use the latter. On the other hand, I've never heard квадратичный трехчлен, whereas квадратный трехчлен is the established term. I think that the rule of square vs quadratic applies in most cases, but perhaps not always, the exceptions being mostly commonly used terms (from school, say, rather than university). Also bilinear forms are translated as квадратичные формы (or билинейные формы) Jun 25 '12 at 17:32
• I agree the exceptions would come from pre-college settings. Although I'm not a native speaker, I am certain that bilinear form is not translated as квадратичная форма; quadratic and bilinear forms are closely related but not the same thing. (If B(v,w) is a bilinear form then Q(v) := B(v,v) is a quadratic form, and if Q(v) is a quadratic form then B(v,w) := (1/2)(Q(v+w)-Q(v)-Q(w)) is a bilinear form such that B(v,v) = Q(v).) If you can find a reference that refers to bilinear forms as квадратичные формы I would be shocked. I'll stick with билинейная форма. :)
– KCd
Jun 25 '12 at 17:43
• @KCd: You're right, I had the wrong recollection that they were the same thing. It's time to refresh my college math, I suppose :) Jun 25 '12 at 18:17

The translation in this particular case would be: квадратное уравнение. In US colleges and schools this is being referred to not as "quadratic formula" but more commonly as "quadratic equation" (and not just by professors from the former USSR).

EDIT: The formula for the solution for this equation normally would be referred as translation you have listed there is no unifying term to describe it.

In general "quadratic" in algebraic expression would generally be translated as "квадратн(ый)(ая)(ое)".

The term Квадраничный as far as I can tell is being used to describe functions in vector spaces(see Wikipedia) or general multidimensional equations(see БСЭ) where terms related to independent variables have power of 2 or are a product of 2 independent variables.

• I'm wondering if you misread my first question. I was asking not about a description of the equation itself, but a description of the formula for the roots of the equation: (-b +/- sqrt(b^2-4ac))/2a. In the US this formula is called the quadratic formula. Referring to this formula for the roots as the "quadratic equation" sounds strange to me. I'm a math professor and if I mention this formula when teaching, say in calculus or abstract algebra, I always refer to it as the "quadratic formula".
– KCd
Jun 25 '12 at 16:31
• Your comment that квадратичный "is not being used" to describe higher degree equations is contradicted by your links, which translate "quadratic form" as квадратичная форма. Maybe you meant to write "is being used..."?
– KCd
Jun 25 '12 at 16:39
• @KCd You're right. It should have been "is being used". As far as formula vs. equation. In English both are correct so I guess it would be a matter of preference. Jun 25 '12 at 16:43
• @KCd You're right I misread your first question. Jun 25 '12 at 17:07