Question

State the Zero-Product Property. Use the property to solve the equation$x\left(x-1\right)=0$

Short answer

The zero product property simply states that if $ab=0$, then either$a=0$ or$b=0$ or both$a$ and$b$ are zero if and if only one or more of the factors is zero and the factor of the given equation are$0$ and $1$.

Step-by-step solution

Step 1. Define Zero product property.

The zero product property simply states that if $ab=0$, then either$a=0$ or$b=0$ or both$a$ and$b$ are zero if and if only one or more of the factors is zero.

Step 2. Example of zero product propert.

Consider the equation.

$x^2+x-20=0$

Factorise the above expression.

$\left(x+5\right)\left(x-4\right)=0$

By the Zero Product property.

$\begin{array}{c}x+5=0\\ x=-5\end{array}$

And,

$\begin{array}{c}x-4=0\\ x=4\end{array}$

Step 3. Solve the given equation.

The given equation is,

$x\left(x-1\right)=0$

By Zero product property,

$x=0$

And,

$\begin{array}{c}x-1=0\\ x=-1\end{array}$

Thus, the zero product property simply states that if $ab=0$, then either$a=0$ or$b=0$ or both$a$ and$b$ are zero if and if only one or more of the factors is zero and the factor of the given equation are$0$ and $1$.