1.
[tex]y = -x^{2}-5x + 6\\\\-x^{2}-5x+6 = 0\\a = -1, \ b = -5, \ c = 6\\\\\Delta = b^{2}-4ac = (-5)^{2}-4\cdot(-1)\cdot6 = 25+24 = 49\\\\\sqrt{\Delta} = \sqrt{49} = 7\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{5-7}{-2} = \frac{-2}{-2} = 1\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{5+7}{-2} = \frac{12}{-2} = -6\\\\Odp. \ B.[/tex]
2.
[tex]|AB| = 4 \ i \ |BC| = 3\\|AC| = ?\\cos\alpha = ?\\\\|AC|^{2}+|CB|^{2} = |AB|^{2}\\\\|AC|^{2} = |AB|^{2}-|BC|^{2}\\\\|AC|^{2} = 4^{2} - 3^{2} = 16-9 = 7\\\\|AC| = \sqrt{7}\\\\\frac{|AC|}{|AB|} = cos\alpha = \frac{\sqrt{7}}{4}\\\\Odp. \ D.[/tex]
3.
[tex]h = 6 \ m\\\alpha = 40^{o}\\l = ?\\\\\frac{l}{h} = ctg\alpha\\\\l = h\cdot ctg\alpha\\\\l = 6\cdot ctg40^{o} = 6 \ m \cdot1,192 \approx 7,2 \ m\\\\Odp. \ B.[/tex]
