query: Find (a,b,c) if $ax^2-bx+c=0$ have roots lying in $(0,1)$ where $a,b,c\in\mathbb{Z_+}$
positive_passages.docid: 144769
positive_passages.text: Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$
negative_passages.docid: 107089
negative_passages.text: finding rational roots of polynomials
negative_passages.docid: 64448
negative_passages.text: Find a quadratic equation with root $x_1^2$ and $x_2^2$
negative_passages.docid: 64955
negative_passages.text: Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$
negative_passages.docid: 54430
negative_passages.text: For $a,b$ coprime, there exists positive integers $x,y$ such that $ax-by=1$
negative_passages.docid: 3206
negative_passages.text: Given $ax^2+by^2+cxy > 0$, what can I deduce about $a$, $b$, and $c$?
negative_passages.docid: 47949
negative_passages.text: If $a$ and $b$ are two roots of $x^4 + x^3 - 1 = 0$ prove that $ab$ is a root of $x^6 + x^4 + x^3 - x^2 - 1$.
negative_passages.docid: 138672
negative_passages.text: Finding Ideals in $\begin{bmatrix} \mathbb{Q} & \mathbb{Q}\\ 0 & 0 \end{bmatrix}$
negative_passages.docid: 140481
negative_passages.text: How to tell if a quartic equation has a multiple root.
negative_passages.docid: 157200
negative_passages.text: Roots of a equation on a complex plane
negative_passages.docid: 16382
negative_passages.text: Find $a$ such that $(x+a)(x+1991)+1=(x+b)(x+c)$ with $a,b,c\in\Bbb Z$
negative_passages.docid: 15730
negative_passages.text: Determine the minimum of $a^2 + b^2$ if $a,b\in\mathbb{R}$ are such that $x^4 + ax^3 + bx^2 + ax + 1 = 0$ has at least one real solution
negative_passages.docid: 125164
negative_passages.text: How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
negative_passages.docid: 146753
negative_passages.text: Find $x$ such that $(x^2 + 4x + 3)^x + (2x + 4)^x = (x^2 + 4x + 5)^x$
negative_passages.docid: 87304
negative_passages.text: Solving for $x$ : $a^x+b^x=c$
negative_passages.docid: 146294
negative_passages.text: 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.
negative_passages.docid: 92701
negative_passages.text: 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 $b+c\neq 4$