Question

Find all x-intercepts of the following function. Write your answer or answers as

Answer 1

Given: The function below

$f(x)=\frac{3x+30}{25x^2-49}$

To determine: All x-intercepts of the given function

The x-intercept is a point where the graph crosses the x-axis

We would substitute the function equal to zero and find the value of x

$\begin{gathered} f(x)=\frac{3x+30}{25x^2-49},f(x)=0 \\ \text{Therefore} \\ \frac{3x+30}{25x^2-49}=0 \\ \text{cross}-\text{ multiply} \\ 3x+30=0 \end{gathered}$$\begin{gathered} 3x=-30 \\ \frac{3x}{3}=\frac{-30}{3} \\ x=-10 \end{gathered}$

Therefore, the coordinate of the x-intercept is (-10, 0)