What Are Zeroes in Polynomial Expressions?

What Are Zeroes in Polynomial Expressions?

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We will now restrict our discussion to polynomials in one variable. For any polynomial expression, the zeroes are those values of the variable for which the polynomial as a whole has zero value. Since we are restricted to the set of Reals, we will always consider zeroes which have real values. This means that even though a polynomial may have zeroes which are complex-valued, we will not be considering them. The following table shows some polynomial expressions and their zeroes:

Polynomial Zeroes
\(x+2\) \(-2\)
\(x^2\;+\;3x\;+2\) \(-1,-2\)
\(x^3\;-\;6x^2\;+\;11x\;-6\) \(1,2,3\)
\(x^4\;+\;1\) \(None\)

We note that some polynomials may have no (real-valued) zeroes.

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