0\\\\x_1=12\; ,\; x_2=4\; \; (teorema\; Vieta)\\\\(x-4)(x-12)>0\; \; \; \; +++(4)---(12)+++\\\\x\in (-\infty ,4)\cup(12,+\infty )\\\\\\2)\; \; 2x-4x^2\leq 0\\\\-2x(2x-1)\leq 0\; \; \to \; \; \; 2x(2x-1)\geq 0\; \; ,\; \; x_1=0\; ,\; x_2=\frac{1}{2}\\\\+++[\, 0\, ]---[\, \frac{1}{2}\, ]+++\qquad x\in (-\infty ,0\, ]\cup [\, \frac{1}{2}\, ,+\infty )\\\\\\3)\; \; x-0,5x^2-10<0\, |\cdot (-2)\\\\x^2-2x+20>0\; \; ,\; \; D/4=1-20=-19<0\; \; \to \; \; x\in (-\infty ,+\infty )" alt="1)\; \; x^2-16x+48>0\\\\x_1=12\; ,\; x_2=4\; \; (teorema\; Vieta)\\\\(x-4)(x-12)>0\; \; \; \; +++(4)---(12)+++\\\\x\in (-\infty ,4)\cup(12,+\infty )\\\\\\2)\; \; 2x-4x^2\leq 0\\\\-2x(2x-1)\leq 0\; \; \to \; \; \; 2x(2x-1)\geq 0\; \; ,\; \; x_1=0\; ,\; x_2=\frac{1}{2}\\\\+++[\, 0\, ]---[\, \frac{1}{2}\, ]+++\qquad x\in (-\infty ,0\, ]\cup [\, \frac{1}{2}\, ,+\infty )\\\\\\3)\; \; x-0,5x^2-10<0\, |\cdot (-2)\\\\x^2-2x+20>0\; \; ,\; \; D/4=1-20=-19<0\; \; \to \; \; x\in (-\infty ,+\infty )" align="absmiddle" class="latex-formula">
![4)\; \; 3x^2\geq 27\\\\3(x^2-9)\geq 0\; \; \to \; \; \; 3(x-3)(x+3)\geq 0\; \; ,\; \; x_1=-3\; ,\; x_2=3\\\\+++[-3\, ]---[\, 3\, ]+++\qquad x\in (-\infty ,-3\, ]\cup [\, 3,+\infty )\\\\\\5)\; \; x^2+5x\geq 14\; \; \to \; \; \; x^2+5x-14\geq 0\\\\D=25+56=81\; \; ,\; \; x_1=-7\; ,\; x_2=2\\\\+++[-7\, ]---[\,2\, ]+++\qquad x\in (-\infty ,-7\, ]\cup [\, 2,+\infty )](https://tex.z-dn.net/?f=4%29%5C%3B%20%5C%3B%203x%5E2%5Cgeq%2027%5C%5C%5C%5C3%28x%5E2-9%29%5Cgeq%200%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20%5C%3B%203%28x-3%29%28x%2B3%29%5Cgeq%200%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20x_1%3D-3%5C%3B%20%2C%5C%3B%20x_2%3D3%5C%5C%5C%5C%2B%2B%2B%5B-3%5C%2C%20%5D---%5B%5C%2C%203%5C%2C%20%5D%2B%2B%2B%5Cqquad%20x%5Cin%20%28-%5Cinfty%20%2C-3%5C%2C%20%5D%5Ccup%20%5B%5C%2C%203%2C%2B%5Cinfty%20%29%5C%5C%5C%5C%5C%5C5%29%5C%3B%20%5C%3B%20x%5E2%2B5x%5Cgeq%2014%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20%5C%3B%20x%5E2%2B5x-14%5Cgeq%200%5C%5C%5C%5CD%3D25%2B56%3D81%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20x_1%3D-7%5C%3B%20%2C%5C%3B%20x_2%3D2%5C%5C%5C%5C%2B%2B%2B%5B-7%5C%2C%20%5D---%5B%5C%2C2%5C%2C%20%5D%2B%2B%2B%5Cqquad%20x%5Cin%20%28-%5Cinfty%20%2C-7%5C%2C%20%5D%5Ccup%20%5B%5C%2C%202%2C%2B%5Cinfty%20%29 "4)\; \; 3x^2\geq 27\\\\3(x^2-9)\geq 0\; \; \to \; \; \; 3(x-3)(x+3)\geq 0\; \; ,\; \; x_1=-3\; ,\; x_2=3\\\\+++[-3\, ]---[\, 3\, ]+++\qquad x\in (-\infty ,-3\, ]\cup [\, 3,+\infty )\\\\\\5)\; \; x^2+5x\geq 14\; \; \to \; \; \; x^2+5x-14\geq 0\\\\D=25+56=81\; \; ,\; \; x_1=-7\; ,\; x_2=2\\\\+++[-7\, ]---[\,2\, ]+++\qquad x\in (-\infty ,-7\, ]\cup [\, 2,+\infty )")