algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations,...
35 KB (5,797 words) - 02:32, 12 December 2024
deriving the formula. Solutions to problems that can be expressed in terms of quadratic equations were known as early as 2000 BC. Because the quadratic equation...
53 KB (6,652 words) - 05:35, 21 December 2024
corresponding quadratic function, of which there can be two, one, or zero. The solutions are described by the quadratic formula. A quadratic polynomial or...
17 KB (2,884 words) - 14:42, 17 December 2024
ax^{2}+bx+c=0,} where a ≠ 0. The quadratic equation on a number x {\displaystyle x} can be solved using the well-known quadratic formula, which can be derived by...
10 KB (1,766 words) - 15:44, 11 November 2024
also used for graphing quadratic functions, deriving the quadratic formula, and more generally in computations involving quadratic polynomials, for example...
21 KB (3,686 words) - 19:00, 27 October 2024
Glomerular filtration rate (redirect from Cockcroft-Gault formula)
9938^{\text{Age}}\ } Another estimation tool to calculate GFR is the Mayo Quadratic formula. This formula was developed by Rule et al., in an attempt to better estimate...
57 KB (8,053 words) - 02:11, 18 December 2024
second degree, or equations or formulas that involve such terms. Quadratus is Latin for square. Quadratic function (or quadratic polynomial), a polynomial...
3 KB (431 words) - 23:54, 14 December 2024
for mathematical formulas. For example, the quadratic formula (which is the solution of the quadratic equation) appears as: The formula is printed in a...
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Discriminant (redirect from Discriminant of a quadratic form)
b^{2}-4ac,} the quantity which appears under the square root in the quadratic formula. If a ≠ 0 , {\displaystyle a\neq 0,} this discriminant is zero if...
41 KB (6,705 words) - 11:39, 1 December 2024
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, 4 x...
33 KB (4,566 words) - 03:12, 28 September 2024
Fibonacci sequence (redirect from Binet's formula)
{5}}\varphi ^{n}} and solved as a quadratic equation in φ n {\displaystyle \varphi ^{n}} via the quadratic formula: φ n = F n 5 ± 5 F n 2 + 4 ( − 1 )...
86 KB (13,062 words) - 12:13, 22 December 2024
root of the quadratic equation x2 + bx + c = 0 for c = 4 and c = 4 × 105. The difference between direct evaluation using the quadratic formula and the approximation...
25 KB (3,245 words) - 16:33, 28 September 2024
In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer...
54 KB (5,557 words) - 19:40, 15 May 2024
Black–Scholes model (redirect from Black-Scholes formula)
_{i}^{2}+\left(r-q-{1 \over {2}}\sigma ^{2}\right)\lambda _{i}-r=0} Using the quadratic formula, the solutions for λ i {\displaystyle \lambda _{i}} are: λ 1 = − (...
65 KB (9,574 words) - 13:34, 4 December 2024
Cubic equation (redirect from Cubic formula)
cubic formula involving the four coefficients, the four basic arithmetic operations, square roots, and cube roots. (This is also true of quadratic (second-degree)...
68 KB (10,291 words) - 02:28, 12 December 2024
This formula only works if it is known in advance that a {\displaystyle a} is a quadratic residue, which can be checked using the law of quadratic reciprocity...
111 KB (8,557 words) - 16:57, 29 November 2024
Factorization (section Quadratic ac method)
{3}{2}})=(3x+2)(2x+3).} Any univariate quadratic polynomial a x 2 + b x + c {\displaystyle ax^{2}+bx+c} can be factored using the quadratic formula: a x 2 + b x + c = a...
41 KB (7,739 words) - 10:07, 6 December 2024
Abel–Ruffini theorem (redirect from Quintic formula)
with the case of lower degree: one has the quadratic formula, the cubic formula, and the quartic formula for degrees two, three, and four, respectively...
28 KB (4,086 words) - 10:43, 12 December 2024
Quartic function (redirect from Quartic formula)
quadratic equation a0z2 + a1z + a2 − 2ma0 = 0. Since x2 − xz + m = 0, the quartic equation P(x) = 0 may be solved by applying the quadratic formula twice...
43 KB (6,849 words) - 07:40, 24 November 2024
Algebraic equation (section Quadratic equations)
Indian mathematician Brahmagupta (597–668 AD) explicitly described the quadratic formula in his treatise Brāhmasphuṭasiddhānta published in 628 AD, but written...
14 KB (2,162 words) - 02:58, 9 October 2023
Brahmagupta (section Brahmagupta's formula)
also credited with the first clear description of the quadratic formula (the solution of the quadratic equation) in his main work, the Brāhma-sphuṭa-siddhānta...
44 KB (5,849 words) - 21:12, 22 December 2024
a_{0}z^{2}+a_{2}z+a_{4}=0\,\!} which is a simple quadratic equation, whose solutions are easily found using the quadratic formula: z = − a 2 ± a 2 2 − 4 a 0 a 4 2 a...
31 KB (6,695 words) - 03:05, 10 December 2024
roots (square roots, cube roots, etc.). A well-known example is the quadratic formula x = − b ± b 2 − 4 a c 2 a , {\displaystyle x={\frac {-b\pm {\sqrt...
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Nevertheless, it contained the first clear description of the quadratic formula (the solution of the quadratic equation). Brāhmasphuṭasiddhānta is one of the first...
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Galois theory (section Quadratic equation)
following examples. Consider the quadratic equation x 2 − 4 x + 1 = 0. {\displaystyle x^{2}-4x+1=0.} By using the quadratic formula, we find that the two roots...
32 KB (4,211 words) - 15:28, 25 November 2024
Algebraic expression (redirect from Algebraic formula)
equation, can always be written as algebraic expressions if n < 5 (see quadratic formula, cubic function, and quartic equation). Such a solution of an equation...
10 KB (1,216 words) - 12:15, 11 October 2024
List of mnemonics (section Quadratic equation)
Visual Thesaurus. Retrieved 2019-07-14. Être Verbs - Mnemonic Devices "Quadratic formula song". Retrieved 22 April 2015. Mnemonics and Gaming "How to use BIDMAS...
57 KB (4,765 words) - 22:45, 13 December 2024
Closed-form expression (redirect from Closed formula)
expression of this object in terms of previous ways of specifying it. The quadratic formula x = − b ± b 2 − 4 a c 2 a . {\displaystyle x={\frac {-b\pm {\sqrt...
16 KB (1,882 words) - 04:35, 19 August 2024
Parallel (operator) (redirect from Product-over-sum formula)
\end{aligned}}} To solve a parallel quadratic equation, complete the square to obtain an analog of the quadratic formula a x 2 ∥ b x ∥ c = ∞ x 2 ∥ b a x =...
59 KB (6,563 words) - 00:31, 30 October 2024
particular, the two solutions of a quadratic equation are conjugate, as per the ± {\displaystyle \pm } in the quadratic formula x = − b ± b 2 − 4 a c 2 a {\displaystyle...
2 KB (355 words) - 00:25, 24 June 2023