To solve the equation using the zero-product property, you need to set each factor in the equation equal to zero and solve for the variable \( n \).
The given equation is:
\[ -8n(10n - 1) = 0 \]
According to the zero-product property, if the product of two factors is zero, then at least one of the factors must be zero. So we set each factor equal to zero:
1. \( -8n = 0 \)
2. \( 10n - 1 = 0 \)
Let's solve each equation separately:
1. \( -8n = 0 \)
Divide both sides by \(-8\):
\[ n = 0 \]
2. \( 10n - 1 = 0 \)
Add 1 to both sides:
\[ 10n = 1 \]
Divide both sides by 10:
\[ n = \frac{1}{10} \]
So the solutions to the equation are:
\[ n = 0 \quad \text{or} \quad n = \frac{1}{10} \]
Thus the answers are:
\[ n = 0 \quad \text{or} \quad n = \frac{1}{10} \]
19.
Solve the equation using the zero-product property.
−8n(10n − 1) = 0
n = 0 or n =
n = 0 or n =
n = or n = mc003-3.jpg
n = or n = mc003-7.jpg
1 answer