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8.Distinguish the terms zero polynomial and zero of a polynomia. |
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Answer» 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 multi set (an un ordered 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+… 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. |
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