$x^{2}-13 x+12$
\(\boxed{x = 12, x = 1}\)
Step 1 :Find the roots of the quadratic equation \(x^2 - 13x + 12 = 0\) using the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 1\), \(b = -13\), and \(c = 12\).
Step 2 :Calculate the roots: \(x_1 = \frac{13 + \sqrt{(-13)^2 - 4(1)(12)}}{2(1)} = 12\) and \(x_2 = \frac{13 - \sqrt{(-13)^2 - 4(1)(12)}}{2(1)} = 1\)
Step 3 :\(\boxed{x = 12, x = 1}\)