[tex]f(x) = x^{2}-6x+5\\\\a = 1, \ b = -6, \ c = 5\\\\\Delta = b^{2}-4ac = (-6)^{2} -4\cdot1\cdot5 = 36 - 20 = 16\\\\\sqrt{\Delta} = \sqrt{16} = 4\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-(-6)-4}{2\cdot1} =\frac{2}{2} = 1\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-(-6)+4}{2} = \frac{10}{2} = 5[/tex]
[tex]p = \frac{-b}{2a} = \frac{-(-6)}{2\cdot1} = \frac{6}{2} = 3\\\\q = \frac{-\Delta}{4a} = \frac{-16}{4\cdot1} = -\frac{16}{4} = -4[/tex]
