a)
[tex]2x^{2}-4x+2 \geq 0\\\\a = 2, \ b = -4, \ c = 2\\\\\Delta =b^{2}-4ac = (-4)^{2}-4\cdot2\cdot2 = 16-16 = 0\\\\x_{0} = \frac{-b}{2a} = \frac{4}{2\cdot2} = \frac{4}{4} = 1\\\\x \in R[/tex]
b)
[tex]x-x^{2}<3-3x^{2}\\\\-x^{2}+3x^{2}+x-3 < 0\\\\2x^{2}+x-3 < 0\\\\a = 2, \ b = 1, \ c = -3\\\\\Delta = b^{2}-4ac =1^{2}-4\cdot2\cdot(-3) = 1+24 = 25\\\\\sqrt{\Delta} = \sqrt{25} = 5\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-1-5}{2\cdot2} = \frac{-6}{4} = -1,5\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-1+5}{4} = \frac{4}{4} = 1\\\\a > 0, \ ramiona \ paraboli \ skierowane \ do \ gory\\\\x \in \ (-1,5; 1)[/tex]
