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 \({x^2} - 3x + 2 = 0\).

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Quadratic Expressions
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Quadratic Expressions
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Quadratic Expressions
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