What is meant by coefficient?
Answers
MATHEMATICS
MATHEMATICSa number which is placed before another quantity and which multiplies it, for example 3 in the quantity 3x
MATHEMATICSa number which is placed before another quantity and which multiplies it, for example 3 in the quantity 3xवह संख्या जो किसी अन्य मात्रा के पहले आकर उससे गुणा की जाती है; गुणांक, जैसे 3x में 3
MATHEMATICSa number which is placed before another quantity and which multiplies it, for example 3 in the quantity 3xवह संख्या जो किसी अन्य मात्रा के पहले आकर उससे गुणा की जाती है; गुणांक, जैसे 3x में 32.
MATHEMATICSa number which is placed before another quantity and which multiplies it, for example 3 in the quantity 3xवह संख्या जो किसी अन्य मात्रा के पहले आकर उससे गुणा की जाती है; गुणांक, जैसे 3x में 32.TECHNICAL
MATHEMATICSa number which is placed before another quantity and which multiplies it, for example 3 in the quantity 3xवह संख्या जो किसी अन्य मात्रा के पहले आकर उससे गुणा की जाती है; गुणांक, जैसे 3x में 32.TECHNICALa number that measures a particular characteristic of a substance
MATHEMATICSa number which is placed before another quantity and which multiplies it, for example 3 in the quantity 3xवह संख्या जो किसी अन्य मात्रा के पहले आकर उससे गुणा की जाती है; गुणांक, जैसे 3x में 32.TECHNICALa number that measures a particular characteristic of a substanceकिसी पदार्थ की विशिष्टता का मापक गुणांक
Step-by-step explanation:
1.MATHEMATICS
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x y).
2. PHYSICS
a multiplier or factor that measures a particular property.
a number or quantity placed (generally) before and multiplying another quantity, as 3 in the expression 3x. Physics. a number that is constant for a given substance, body, or process under certain specified conditions, serving as a measure of one of its properties: coefficient of friction.
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as {\displaystyle a}, {\displaystyle b}and {\displaystyle c}).[1][2][3] In the latter case, the variables appearing in the coefficients are often called parameters, and must be clearly distinguished from the other variables.
For example, in
{\displaystyle 7x^{2}-3xy+1.5+y,}
the first two terms have the coefficients 7 and −3, respectively. The third term 1.5 is a constant coefficient. The final term does not have any explicitly-written coefficient factor that would not change the term; the coefficient is thus taken to be 1 (since variables without number have a coefficient of 1[2]).
In many scenarios, coefficients are numbers (as is the case for each term of the above example), although they could be parameters of the problem—or any expression in these parameters. In such a case, one must clearly distinguish between symbols representing variables and symbols representing parameters. Following René Descartes, the variables are often denoted by x, y, ..., and the parameters by a, b, c, ..., but this is not always the case. For example, if y is considered a parameter in the above expression, then the coefficient of x would be −3y, and the constant coefficient (always with respect to x) would be 1.5 + y.
When one writes
{\displaystyle ax^{2}+bx+c,}
it is generally assumed that x is the only variable, and that a, b and c are parameters; thus the constant coefficient is c in this case.
Similarly, any polynomial in one variable x can be written as
{\displaystyle a_{k}x^{k}+\dotsb +a_{1}x^{1}+a_{0}}
for some positive integer {\displaystyle k}, where {\displaystyle a_{k},\dotsc ,a_{1},a_{0}} are coefficients; to allow this kind of expression in all cases, one must allow introducing terms with 0 as coefficient. For the largest {\displaystyle i} with {\displaystyle a_{i}\neq 0} (if any), {\displaystyle a_{i}} is called the leading coefficient of the polynomial. For example, the leading coefficient of the polynomial
{\displaystyle \,4x^{5}+x^{3}+2x^{2}}
is 4.
Some specific coefficients that occur frequently in mathematics have dedicated names. For example, the binomial coefficients occur in the expanded form of {\displaystyle (x+y)^{n}}, and are tabulated in Pascal's triangle.
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