Any quadratic polynomial over the complex numbers ( polynomials of the form where,, and ∈ ) can be factored into an expression with the form using the quadratic formula.

Any problem that had to be solved by random, brute-force search, could now have a quadratic speedup.

Any n × n real symmetric matrix A determines a quadratic form q < sub > A </ sub > in n variables by the formula

Any smooth function of one variable approximates a quadratic function when examined near enough to its minimum point ; and therefore the force — which is the derivative of energy with respect to displacement — will approximate a linear function.

Any prime number p gives rise to an ideal pO < sub > K </ sub > in the ring of integers O < sub > K </ sub > of a quadratic field K.

Any n-dimensional formal group law gives an n dimensional Lie algebra over the ring R, defined in terms of the quadratic part F < sub > 2 </ sub > of the formal group law.

Any single-variable quadratic polynomial may be written as

Any non-singular matrix S of the same size is said to transform A into another symmetric matrix B = SAS < sup > T </ sup >, also of order n, where S < sup > T </ sup > is the transpose of S. If A is the coefficient matrix of some quadratic form of R < sup > n </ sup >, then B is the matrix for the same form after the change of coordinates defined by S.

Any càdlàg finite variation process X has quadratic variation equal to the sum of the squares of the jumps of X.

Any polynomial may be decomposed into the product of a constant by a product of irreducible polynomials.

Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.

Any polynomial can be easily expressed as a power series around any center c, albeit one with most coefficients equal to zero.

* Any polynomial ( real or complex ) is an analytic function.

Any polynomial written in standard form has a unique constant term, which can be considered a coefficient of x < sup > 0 </ sup >.

Any rational function of a real variable can be written as the sum of a polynomial function and a finite number of algebraic fractions.

Any polynomial in D with function coefficients is also a differential operator.

Any monic polynomial is the characteristic polynomial of some matrix.

Any general polynomial of degree n

Any holomorphic modular form for the modular group can be written as a polynomial in and.

Any polynomial, and more generally any rational function p ( x )/ q ( x ) where p and q are polynomials, transforms the Riemann sphere by mapping it to itself.

Any posse riding down the street to demand Blue Throat's surrender would be wiped out with one deadly burst of fire.

Any abilities I may have were achieved in their present shape from experience in sharing in the growth and control of my business, coupled with raising my family.

Any attempt to reconcile this statement of the central issue in the campaign of 1956 with the nature of the man who could not conceive it as the central issue will at least resolve our confusions about the chaotic and misleading results of the earnestness of both doctors and President in a situation which should never have arisen.

Any claimant whose claim is denied, or is approved for less than the full amount of such claim, shall be entitled, under such regulations as the Commission may prescribe, to a hearing before the Commission, or its duly authorized representatives, with respect to such claim.

Any irregularity on the piston heads will make it impossible, with normal means, to determine the final combustion chamber volume because the volume displaced by the piston heads cannot be readily computed.

Any reputable French interne can supply you with a dozen similar instances, and I'll presently recount a case out of my own personal experience, but, for the moment, let's resume our catalogue.

Any of the antithyroid drugs, of either type, if given in large enough doses for a long period of time will cause goitre, owing to inhibition of thyroid hormone synthesis, with production of hypothyroidism.

Any adjustments which are made, Mr. Grenier said earlier this month, will appear on the balance of the tax bill since most of the town's taxpayers take the option of paying quarterly with the balance due next year.

Any shareholder of any of these funds who finds a mistake in his account certainly should get in touch with the bank.

Any musician playing Beethoven here, where Beethoven was born, is likely to examine his own interpretations with special care.

* Any ring of matrices with coefficients in a commutative ring R forms an R-algebra under matrix addition and multiplication.

Most of the C code being written nowadays is based on ANSI C. Any program written only in standard C and without any hardware dependent assumptions is virtually guaranteed to compile correctly on any platform with a conforming C implementation.

Any company incorporating Bluetooth wireless technology into products, using the technology to offer goods and services or simply re-branding a product with Bluetooth technology must become a member of the Bluetooth SIG.

Any codex of Bede's Easter cycle is normally found together with a codex of his " De Temporum Ratione ".

Love and Erlandson continued to pursue with the band, and released the single " Be A Man "— an outtake from the Celebrity Skin sessions — for the soundtrack of the Oliver Stone film Any Given Sunday ( 1999 ).

Any differential area with normal vector of a given internal surface area, bounding a portion of the body, experiences a contact force arising from the contact between both portions of the body on each side of, and it is given by

# Any collection of closed subsets of X with the finite intersection property has nonempty intersection.

Any season ticket holder could put themselves forward for election, with a certain number of nominations, and votes were cast by all season ticket holders over the age of 18.

Any pellets which are too small to be finished granules of couscous and fall through the sieve will be again rolled and sprinkled with dry semolina and rolled into pellets.

Any successes that the Nationalists did make, however, were met with constant political and military upheavals.

Any piece of DNA with the point centromere DNA sequence on it will typically form a centomere if present in the appropriate species.

# Any experience which is inconsistent with the organization of the structure of the self may be perceived as a threat, and the more of these perceptions there are, the more rigidly the self structure is organized to maintain itself.

Any rational number with a denominator whose only prime factors are 2 and / or 5 may be precisely expressed as a decimal fraction and has a finite decimal expansion.

Any units of angular measure can be used for declination, but it is customarily measured in the degrees ( ° ), minutes ( ' ), and seconds ( " ) of sexagesimal measure, with 90 ° equivalent to circle.

Any ellipse can be obtained by rotation and translation of a canonical ellipse with the proper semi-diameters.