algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations,...

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...

corresponding quadratic function, of which there can be two, one, or zero. The solutions are described by the quadratic formula. A quadratic polynomial or...

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...

second degree, or equations or formulas that involve such terms. Quadratus is Latin for square. Quadratic function (or quadratic polynomial), a polynomial...

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...

also used for graphing quadratic functions, deriving the quadratic formula, and more generally in computations involving quadratic polynomials, for example...

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...

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...

for mathematical formulas. For example, the quadratic formula (which is the solution of the quadratic equation) appears as: The formula is printed in a...

{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 )...

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...

cubic formula involving the four coefficients, the four basic arithmetic operations, square roots, and cube roots. (This is also true of quadratic (second-degree)...

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...

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...

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...

{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...

Indian mathematician Brahmagupta (597–668 AD) explicitly described the quadratic formula in his treatise Brāhmasphuṭasiddhānta published in 628 AD, but written...

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...

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...

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...

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...

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...

discussed the use of negative numbers to produce a general form quadratic formula similar to the one in use today. In the 9th century, Islamic mathematicians...

Nevertheless, it contained the first clear description of the quadratic formula (the solution of the quadratic equation). Brāhmasphuṭasiddhānta is one of the first...

_{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 = − (...

numbers first arise in the teaching of quadratic equations and the quadratic formula. For example, the quadratic equation x 2 + x + 1 = 0 {\displaystyle...

that is a quadratic character modulo of an odd prime number p: its value at a (nonzero) quadratic residue mod p is 1 and at a non-quadratic residue (non-residue)...

which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that...

\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 =...