Questions: Quadratic Functions and Equations Solving an equation written in factored form Solve. (4-v)(4v-9)=0 v=

Solution Steps

To solve the equation \((4-v)(4v-9)=0\), we need to use the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for \(v\).

1. Set each factor equal to zero: \(4-v=0\) and \(4v-9=0\).
2. Solve each equation for \(v\).

Given the equation \((4-v)(4v-9)=0\), we use the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero: \[ 4 - v = 0 \quad \text{and} \quad 4v - 9 = 0 \]

Solve the first equation for \(v\): \[ 4 - v = 0 \implies v = 4 \]

Solve the second equation for \(v\): \[ 4v - 9 = 0 \implies 4v = 9 \implies v = \frac{9}{4} \]

Final Answer