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Solve for $n$ . $\newline$ $n(n - 5) = 0$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $n =$ _ or $n =$ _

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Solve a quadratic equation using the zero product property

Full solution

Q. Solve for

n

.

\newline

n(n - 5) = 0

\newline

Write your answers as integers or as proper or improper fractions in simplest form.

\newline

n =

_____ or

n =

_____

Apply Zero Product Property: Apply the zero product property to the equation $n(n - 5) = 0$ . $\newline$ The zero product property states that if a product of two factors is zero, then at least one of the factors must be zero. $\newline$ Therefore, we set each factor equal to zero separately. $\newline$ $n = 0$ or $n - 5 = 0$
Solve $n = 0$ : Solve the first equation $n = 0$ . This equation is already solved, and it tells us that one possible value for $n$ is $0$ . $n = 0$
Solve $n - 5 = 0$ : Solve the second equation $n − 5 = 0$ . $\newline$ To find the value of $n$ , we add $5$ to both sides of the equation. $\newline$ $n − 5 + 5 = 0 + 5$ $\newline$ $n = 5$

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\newline

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