can a polynomial have more than one zero According to the Fundamental Theorem every polynomial function has at least one complex zero Every polynomial function with degree greater than 0 has at least one complex zero Allowing for multiplicities a polynomial function will
In mathematics a polynomial is a mathematical expression consisting of indeterminates also called variables and coefficients that involves only the operations of addition subtraction multiplication and exponentiation to nonnegative integer powers and has a finite number of terms An example of a polynomial of a single indeterminate x is x 4x 7 An example with three indeterminates is x 2xyz yz 1 Polynomial are sums and differences of polynomial terms For an expression to be a polynomial term any variables in the expression must have whole number powers or else the understood power of 1 as in x1 which is
can a polynomial have more than one zero
can a polynomial have more than one zero
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Therefore b a is the only zero of p x ax b We can also say that a linear polynomial has only one zero Observations A zero of a polynomial need not be 0 0 may be a zero of a polynomial Every linear polynomial has one and All polynomial functions of positive odd order have at least one zero this follows from the fundamental theorem of algebra while polynomial functions of positive even order may not have a zero for example x 4 1 x4 1 has no real zero
According to the Fundamental Theorem of Algebra every polynomial function has at least one complex zero Every polynomial function with degree greater than 0 has at least one complex zero Allowing for multiplicities a polynomial function The Fundamental Theorem of Algebra guarantees us at least one complex zero z 1 and as such the Factor Theorem guarantees that f x factors as f x left x
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According to the Fundamental Theorem every polynomial function with degree greater than 0 has at least one complex zero Allowing for multiplicities a polynomial function will have the same number of factors as its degree The number of real zeros of a polynomial is less than or equal to the degree order of the polynomial For instance f x x 2 1 order 2 has two real zeros g x x 2
Suppose f x a n x n a n 1 x n 1 ldots a 1 x a 0 is a polynomial of degree n with n geq 1 and a 0 a 1 ldots a n are integers If r is a rational Can a Polynomial have more than One Zero Yes a polynomial can have more than one zero in fact the polynomial of n degrees can have at most n real zeros What is the
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can a polynomial have more than one zero - All polynomial functions of positive odd order have at least one zero this follows from the fundamental theorem of algebra while polynomial functions of positive even order may not have a zero for example x 4 1 x4 1 has no real zero