Determine the roots of the function: (b) $f(x)=x^{2}-x-3$

Step 1 ：Given the function \(f(x)=x^{2}-x-3\), we are to find the roots of the function.

Step 2 ：We can find the roots of a quadratic function using the quadratic formula, which is given by: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where a, b, and c are the coefficients of the quadratic equation \(ax^2 + bx + c = 0\). In this case, a = 1, b = -1, and c = -3.

Step 3 ：Substituting the values of a, b, and c into the quadratic formula, we get the roots of the function as \(x1 = 2.302775637731995\) and \(x2 = -1.3027756377319946\).

Step 4 ：Final Answer: The roots of the function \(f(x)=x^{2}-x-3\) are \(\boxed{2.302775637731995}\) and \(\boxed{-1.3027756377319946}\).