Question

What are the zeros of the function f(x) = (2x-1) (x+4)?

Answer 1

The zeros of a function are the values of x when f(x) is equal to 0. To find the zeros of a function when it is in factored form, we set the factor equal to 0:

`\begin{gathered} f(x)=(2x-1)(x+4) \\ 0=(2x-1)(x+4) \\ 0=2x-1\text{ and }0=x+4 \end{gathered}`

Now, we solve for x each factor:

`\begin{gathered} 0=2x-1 \\ \text{ Add 1 from both sides of the equation} \\ 0+1=2x-1+1 \\ 1=2x \\ \text{ Divide by 2 from both sides} \\ (1)/(2)=(2x)/(2) \\ (1)/(2)=x \end{gathered}`
`\begin{gathered} 0=x+4 \\ \text{ Subtract 4 from both sides} \\ 0-4=x+4-4 \\ -4=x \end{gathered}`

Therefore, the zeros of the function are -4 and 1/2.