1.
[tex]f(x) = 6x^2 + x - 1\\f(x) = 0\\6x^2+x-1 = 0\\\Delta = 1 - 4\cdot (-1)\cdot (6) = 1 + 24 = 25\Rightarrow \sqrt{\Delta} = 5\Rightarrow x_{1,2} = \frac{-1 \pm 5}{2\cdot 6} \Rightarrow\\x_1 = \frac{-6}{12} = -\frac{1}{2}\\x_2 = \frac{4}{12} = \frac{1}{3}[/tex]
b)[tex]Ec: x = \frac{-b}{2a} = \frac{-1}{2\cdot 6}\Rightarrow x = \frac{-1}{12}[/tex]
c)[tex]a > 0 \Rightarrow f(x) < 0, x \in (-\frac{1}{2}, \frac{1}{3})[/tex]
2.a)
[tex]\vec{AB} = (x_B - x_A)\cdot \vec{i} + (y_B - y_A)\cdot \vec{j} = (-2 -1)\vec{i} + (-1 -2)\vec{j} = -3\vec{i} -3\vec{j}[/tex]
b)[tex]13 = \sqrt{5^2 + a^2}\Rightarrow 25 + a^2 = 169\Rightarrow a^2 = 144\Rightarrow a = \pm \sqrt {144} = \pm 12[/tex]
3.a)
[tex]\frac{3\pi}{4} \in (\frac{\pi}{2}, \pi)\Rightarrow \frac{3\pi}{4} \in C_2[/tex]
b)
[tex]\frac{3\pi}{5} = 0.6\pi \in (\frac{\pi}{2}, \pi)\Rightarrow \frac{3\pi}{5} \in C_2[/tex]
