what is the difference between zero polynomial and zero of polynomial
what is the difference between zero polynomial and zero of polynomial
A “zero of a polynomial” is a value (a number) at which the polynomial evaluates to zero. For example, the polynomial x^2–3x+2 has 1 and 2 as its zeros.
The zeros of a polynomial are commonly called its “roots”. Every polynomial has its own multiset (an unordered list) of zeros. In fact, a polynomial is uniquely defined by its zeros, up to scaling by a constant value.
The “zero polynomial” is a specific polynomial, written 0. All its coefficients are zero, and treated as a function it’s a constant function. We could write this polynomial as 0+0x+0x^2+0x^3+…0
to emphasize that it is a polynomial, but it’s a little strange because its degree is undefined. (The constant 1 is also a polynomial, but it has degree zero— a “zero-degree polynomial” and the “zero polynomial” are different.)
The “zeros of the zero polynomial” are all numbers, since substituting any value in for xx results in the value zero
Like if satisfied
A “zero of a polynomial” is a value (a number) at which the polynomial evaluates to zero. For example, the polynomial x^2–3x+2 has 1 and 2 as its zeros.
The zeros of a polynomial are commonly called its “roots”. Every polynomial has its own multiset (an unordered list) of zeros. In fact, a polynomial is uniquely defined by its zeros, up to scaling by a constant value.
The “zero polynomial” is a specific polynomial, written 0. All its coefficients are zero, and treated as a function it’s a constant function. We could write this polynomial as 0+0x+0x^2+0x^3+…0
to emphasize that it is a polynomial, but it’s a little strange because its degree is undefined. (The constant 1 is also a polynomial, but it has degree zero— a “zero-degree polynomial” and the “zero polynomial” are different.)
The “zeros of the zero polynomial” are all numbers, since substituting any value in for xx results in the value zero
Like if satisfied
