Both roots may be valid, or, depending on the problem, it may be that one root or the other may be rejected on mathematical or physical grounds. Dividing through by the variable \(x\) will result in o...Both roots may be valid, or, depending on the problem, it may be that one root or the other may be rejected on mathematical or physical grounds. Dividing through by the variable \(x\) will result in one solution, \(x=a\); the solution \(x=0\) has been lost. Instead of dividing through by the variable \(x\), the proper procedure is to factor out an \(x\) : Since the product on the left-hand side is zero, it follows that either \(x=0\) or \(x-a=0\), and we retain both roots.
