Question

solve for a.
a(a - 1) = 0
write your answers as integers or fractions.
a = or a =

Explanation:

Step1: Apply zero - product property

The zero - product property states that if \(ab = 0\), then either \(a=0\) or \(b = 0\) (or both). For the equation \(a(a - 1)=0\), we can set each factor equal to zero.
First, set \(a=0\). When \(a = 0\), the left - hand side of the equation \(a(a - 1)\) becomes \(0\times(0 - 1)=0\), which satisfies the equation \(a(a - 1)=0\).

Step2: Solve for the other factor

Set the second factor \(a - 1=0\). To solve for \(a\), we add 1 to both sides of the equation \(a - 1=0\). Using the addition property of equality, if we add 1 to both sides, we get \(a-1 + 1=0 + 1\), which simplifies to \(a = 1\). When \(a = 1\), the left - hand side of the equation \(a(a - 1)\) becomes \(1\times(1 - 1)=1\times0 = 0\), which also satisfies the equation \(a(a - 1)=0\).

Answer:

\(a = 0\) or \(a=1\)