What Are Roots in Polynomial Expressions?

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.