Zad 1. Rozwiąż nierówność e) [latex]4x+5 extgreater x^{2} [/latex] f) [latex]2 x^{2} + 5x extgreater 3[/latex] g) [latex]6 x^{2} - x extgreater 12[/latex][latex] h) 3x + 8 geq frac{1}{2} x^{2} [/latex]

[latex]e)4x+5>x^2\-x^2+4x+5>0\Delta=16+20=36\sqrt{Delta}=6\x_1=frac{-4-6}{-2}=5\x_2=frac{-4+6}{-2}=-1\\underline{---}(-1)underline{+++}(5)underline{---}\\xin(-1,5) \\f)2x^2+5x>3\2x^2+5x-3>0\Delta=25+24=49\sqrt{Delta}=7\x_1=frac{-5-7}{4}=-3\x_2=frac{-5+7}{4}=frac{1}{2}\\underline{+++}(-3)underline{---}(frac{1}{2})+++\\xin(-infty,-3)cup(frac{1}{2},+infty) \\g)6x^2-x>12\6x^2-x-12>0\Delta=1+288=289\sqrt{Delta}=17\x_1=frac{1-17}{12}=frac{4}{3}\x_2=frac{1+17}{12}=frac{3}{2}\\underline{+++}(frac{4}{3})underline{---}(frac{3}{2})underline{+++}\\xin(-infty,frac{4}{3})cup(frac{3}{2},+infty) \\h)3x+8geq frac{1}{2}x^2\-frac{1}{2}x^2+3x+8geq 0/*(-2)\x^2-6x-16leq 0\Delta=36+64=100\sqrt{Delta}=10\x_1=frac{6-10}{2}=-2\x_2=frac{6+10}{2}=8\\underline{+++}<-2>underline{---}<8>underline{+++}\\xin,-2,8>[/latex]