3.
[tex]f(x) = \frac{2}{3}x^{2}-2x-12\\\\f(x) = 0\\\\\frac{2}{3}x^{2}-2x-12 = 0 \ \ /\cdot3\\\\2x^{2}-6x-36 = 0\\\\\Delta} = b^{2}-4ac = (-6)^{2}-4\cdot2\cdot(-36) = 36+288 = 324\\\\\sqrt{\Delta} = \sqrt{324} = 18\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-(-6)-18}{2\cdot2} = \frac{-12}{4} = -3\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-(-6)+18}{4} = \frac{24}{4} = 6[/tex]
Wzór funkcji w postaci iloczynowej:
[tex]f(x) =a (x-x_1)(x-x_2)\\\\a = \frac{2}{3}, \ x_1 = -3, \ x_2 = 6\\\\\boxed{f(x) =\frac{2}{3}(x+3)(x-6)}[/tex]
