f)
14x^3+2x^2-21x-3>0
dzielniki 3:p=-1,1,-3,3}
dzielniki 14 q=-1,1,-2,2,-7,7,-14,14
\frac{p}{q}=-\frac{1}{7}
14*(-\frac{1}{7})^3+2*(\frac{1}{7})^2-21*(-\frac{1}{7})-3=14*(-\frac{1}{343})+\frac{2}{49}+3-3=-\frac{2}{49}+\frac{2}{49}=0
-\frac{1}{7} jest pierwiastkiem [x-(-\frac{1}{7})]=(x+\frac{1}{7})=(7x+1)
14x^3+2x^2-21x-3:(7x+1)=2x^2-3
-14x^2-2x^2
-----------------
\\\\\\\\\\\-21x-3
\\\\\\\\\\\+21x+3
---------------
\\\\\\\\0
14x^3+2x^2-21x-3>0
(7x+1)(2x^2-3)>0
x=-\frac{1}{7}\vee 2x^2-3=0
2x^2=3
x^2=\frac{3}{2}
x=\sqrt{\frac{3}{2}} \vee x=-\sqrt{\frac{3}{2}}
x=\frac{\sqrt3}{\sqrt2} \vee x=-\frac{\sqrt3}{\sqrt2}
x=\frac{\sqrt3*\sqrt2}{\sqrt2*\sqrt2}=\frac{\sqrt6}{2} \vee x=-\frac{\sqrt6}{2}
x\in (-\frac{\sqrt6}{2};-\frac{1}{7})\cup (\frac{\sqrt6}{2};+\infty)
http://www.wolframalpha.com/input/?i=14x%5E3%2B2x%5E2-21x-3%3E0