The equation $2x^2+ax+(b+3)=0$ has real roots. Find the minimum value of $a^2+b^2$
843
High school quadratic inequality question
26287
Find $\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$ if $a+b+c=0$
45775
In a $\triangle ABC,$ Evaluation of minimum value of $\cot^2 A+\cot^2 B+\cot^2 C$
60206
Find minimum of $P=\frac{\sqrt{3(2x^2+2x+1)}}{3}+\frac{1}{\sqrt{2x^2+(3-\sqrt{3})x +3}}+\frac{1}{\sqrt{2x^2+(3+\sqrt{3})x +3}}$
144769
Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$
61533
Solution af a system of 2 quadratic equations
43470
Prove: For odd integers $a$ and $b$, the equation $x^2 + 2 a x + 2 b = 0$ has no integer or rational roots.
27278
Let $\alpha \in \overline{\Bbb Q}$ a root of $X^3+X+1\in\Bbb Q[X]$. Calculate the minimum polynomial of $\alpha^{-1}$ en $\alpha -1$.
33105
Find the value of $a^2-b^2+c^2$
39179
Why is $(0, 0)$ not a minimum of $f(x, y) = (y-3x^2)(y-x^2)$?
76716
Solve an equation in $\mathbb{R}^+$
147442
Quadratic Diophantine Equation $x^2 + axy + y^2 = z^2$
3206
Given $ax^2+by^2+cxy > 0$, what can I deduce about $a$, $b$, and $c$?
36331
One root common to $ax^2+2bx+c=0$ and $dx^2+2ex+f=0$
99739
The diophantine equation $x^2+y^2=3z^2$
148983
If $a$, $b$, $c$ are the roots of $x^3-6x^2+3x+1=0$, find all possible values of $a^2b+b^2c+c^2a$
44020
Probability of $x^2+bx+c=0$ having real roots