# Zeroes and Roots

Consider the expression** **\(Q\left( x \right)\,\,:\,\,{x^2} - 1\). The value of this expression is 0 when the value of \(x\) is either 1 or \( - 1\). We will say that \(x = 1\) and \(x = - 1\) are the ** zeroes** of \(Q\left( x \right)\). The zeroes of an expression are those values of the variable for which the expression’s value becomes zero.

**Roots **of an equation, on the other hand, are those values of the variable which

*satisfy*the equation. For example, consider the quadratic equation \({x^2} - 1 = 0\). The roots of this equation are \(x = 1\) and \(x = - 1\).

Do not confuse the two terms zeroes and roots. Keep in mind that:

Zeroes are of expressions

Roots are of equations

If you see phrases like *“zeroes of an equation”* or “*roots of an expression”*, you should immediately realize their incorrectness.

The zeroes of any expression \(P\left( x \right)\) will the same as the roots of the equation \(P\left( x \right) = 0\). For example, the zeroes of the quadratic expression \(Q\left( x \right)\,\,:\,\,{x^2} - 3x + 2\) are the same as the roots of the quadratic equation \(Q\left( x \right) = 0\), that is, of the equation \({x^2} - 3x + 2 = 0\).