[tex]f(x) = x^{2}-2x-3\\g(x) = 3x^{2}+2x-1[/tex]
Miejsca zerowe funkcji f(x):
[tex]x^{2}-2x -3 = 0\\\\a = 1, \ b = -2, \ c = -3\\\\\Delta = b^{2}-4ac = (-2)^{2}-4\cdot1\cdot(-3) =4+12 = 16\\\\\sqrt{\Delta} = \sqrt{16} = 4\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{2-4}{2\cdot1} = \frac{-2}{2} = -1\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{2+4}{2} = \frac{6}{2} = 3[/tex]
Miejsca zerowe funkcji g(x):
[tex]3x^{2}+2x-1 = 0\\\\a = 3, \ b = 2, \ c = -1\\\\\Delta = b^{2}-4ac = 2^{2}-4\cdot3\cdot(-1) = 4+12 = 16\\\\\sqrt{\Delta} = \sqrt{16} = 4\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-2-4}{2\cdot3} = \frac{-6}{6} = -1\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-2+4}{6} = \frac{2}{6} = \frac{1}{3}\\\\\boxed{x = -1}[/tex]
Odp. Wspólnym miejscem zerowym jest x = -1.
