What Are Roots in Polynomial Expressions?

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A distinction must be made between zeroes and roots. Zeroes correspond to expressions, and roots correspond to equations. For example, the equation $$2x + 3 = 0$$ is different from the expression $$2x + 3,$$ even though the root of the first is equal to the zero of the second.

Thus, always remember that a zero is a value of the variable for which the value of the expression is 0, while a root is a value of the variable for which both sides of the equation are equal. As another example, note that that zero of the expression $$2x + 3$$ is $$x = - \frac{3}{2}$$ while the root of the equation $$2x + 3 = 5$$ is $$x = 1$$.

Suppose that you read the statement: $$x = 2$$ is a zero of $$2x - 4 = 0$$. You should immediately see that the statement uses incorrect terminology: $$x = 2$$ is a root of $$2x - 4 = 0$$, and not a zero.

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