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

Transcript text: Quadratic Functions and Equations Solving an equation written in factored form Solve. \[ (4-v)(4 v-9)=0 \] \[ v= \]

Solution

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 \(v\).

Solution Approach

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

Step 1: Apply the Zero-Product Property

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: \[ 4 - v = 0 \quad \text{and} \quad 4v - 9 = 0 \]

Step 2: Solve Each Equation

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

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