Step 1 :Given the quadratic equation: \(f(x) = x^2 - 2x - 3\)
Step 2 :Use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Step 3 :Substitute the coefficients: a = 1, b = -2, c = -3
Step 4 :Calculate the discriminant: \(b^2 - 4ac = 16\)
Step 5 :Find the roots: \(x = \frac{-(-2) \pm \sqrt{16}}{2(1)}\)
Step 6 :\(x = \frac{2 \pm 4}{2}\)
Step 7 :\(x = 3.0\) and \(x = -1.0\)
Step 8 :\(\boxed{x = 3.0, x = -1.0}\)