Question

question #6
the graph of f(x)=\frac{1}{20}(x^{4}-5x^{3}-x^{2}+11x - 30) is shown below. determine the number of real roots of f(x).

Explanation:

Step1: Recall root - definition

The real roots of a function \(y = f(x)\) are the \(x\) - values for which \(f(x)=0\), which are the \(x\) - intercepts of the graph of the function.

Step2: Count \(x\) - intercepts

By observing the given graph of \(y = f(x)=\frac{1}{20}(x^{4}-5x^{3}-x^{2}+11x - 30)\), we count the number of times the graph crosses or touches the \(x\) - axis. The graph crosses the \(x\) - axis at two points.

Answer:

2