$x^{3}+ax^2+bx+c$ has all roots negative real numbers and a<3. Establish an inequality between only b and c
92701
let $a,b,c \in\mathbb{R} ,a<3$ and all roots $p(x)=x^3+ax^2+bx+c=0$ be negative . then prove that $b+c\neq 4$
134535
Inequality $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \geq a + b+ c$ when $abc = 1$
66261
Inequalities help: $(a^3+b^3)^2\leq (a^2+b^2)(a^4+b^4)$
44247
For $a^3+b^3+c^3=3$ prove that $a^4b+b^4c+c^4a\leq3$
25870
Prove that $0 \leq ab + ac + bc - abc \leq 2.$
45090
Given any positive real numbers $a,b,c$, we have $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
120390
An inequality involving 4 real or complex numbers
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
144769
Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$
146294
Find all positive integers $a,b$ such that each of the equations $x^2-ax+b=0$ and $x^2-bx+a=0$ has distinct positive integral roots.
2504
Inequality $\left|\,x_1\,\right|+\left|\,x_2\,\right|+\cdots+\left|\,x_p\,\right|\leq\sqrt{p}\sqrt{x^2_1+x^2_2+\cdots+x^2_p}$
28499
Inequality.$\sqrt{\frac{2a}{b+c}}+\sqrt{\frac{2b}{c+a}}+\sqrt{\frac{2c}{a+b}} \leq 3$
106011
Proving it has all real roots
45711
Inequality with complex numbers
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
157710
$x^{3}-x-2=0$ how do I find the roots?