Answer
Zeros of $f(x)$: $x=2,7$
Work Step by Step
$f(x)=\frac{x^2-9x+14}{4x}$
The zeros of a function are the x-values for when y-values equal zero. In other words, zeros are when $y=f(x)=0$. Since we are solving for the zeros of $f(x)$, set the function $f(x)=\frac{x^2-9x+14}{4x}$ equal to zero. We get the following equation:
$\frac{x^2-9x+14}{4x}=0$
First, multiply both sides of the equation by $4x$ to simplify the denominator:
$\frac{x^2-9x+14}{4x}(4x)=0(4x)$
$x^2-9x+14=0$
Now factor the left side of the equation by finding two numbers that multiply to get 14 and add to get -9. These two numbers are -2 and -7. So the factored left side looks as follows:
$(x-2)(x-7)=0$
Next, you can see that the above equation holds true when $x-2=0$ or $x-7=0$. Solve each of those two equations individually.
$x-2=0$
Add 2 to both sides.
$x-2+2=0+2$
$x=2$
Now for the other equation:
$x-7=0$
Add 7 to both sides.
$x-7+7=0+7$
$x=7$
So, the zeros of $f(x)$ are $x=2,7$
