a) [latex]-x^{3}+2x^{2}+4xleq0\ x(x^2 - 2x - 4)geq0\ Delta = 4 + 16 = (2sqrt{5})^2\ x(x - 1 - sqrt{5})(x + 1 + sqrt{5}) geq 0\ x in (-infty, - 1 - sqrt{5}> cup <0, 1 + sqrt{5}>[/latex] b) [latex]-x^{3}+2x^{2}+4x>3\ -x^{3}+2x^{2}+4x-3>0\[/latex] schemat Hornera - | -1| 2 | 4 | -3 3| -1| -1 | 1| 0 [latex](x - 3)(-x^2 - x+1)>0\ (x - 3)(x^2 + x-1)<0\ Delta = 1 + 4\ (x - 3)left(x - frac{-1-sqrt{5}}{2}
ight)left(x - frac{-1+sqrt{5}}{2}
ight)<0\ x in left(-frac{1+sqrt{5}}{2}, frac{-1+sqrt{5}}{2}
ight)cup(3, infty)[/latex] c) [latex]x^{3}-6x^{2}+12xleq8\ x^{3}-6x^{2}+12x-8leq0\ x^{3}-3*2x^{2}+3*2^2x-2^3leq0\ (x - 2)^3leq0\ x = 2[/latex] d) [latex]2x^{3}-3x^{2}-10x+15leq0[/latex] schemat Hornera ---- | 2 |-3|-10| 15 3/2| 2 | 0 | -10| 0 [latex](x - 1,5)(2x^2 - 10) leq 0\ (x - 1,5)(x^2 - 5) leq 0\ (x - 1,5)(x - sqrt{5})(x + sqrt{5}) leq 0\ x in <-sqrt{5}; 1,5> cup
