query: If the coefficients of the quadratic equation $ax^2+bx +c$ are u.i.i.d ran variates in $(0,1)$ what is the probability of roots being real?
positive_passages.docid: 50084
positive_passages.text: Probability that a quadratic polynomial with random coefficients has real roots
negative_passages.docid: 121759
negative_passages.text: If this equation in x has real roots find the value of a and b.
negative_passages.docid: 144769
negative_passages.text: Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$
negative_passages.docid: 151961
negative_passages.text: Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
negative_passages.docid: 54093
negative_passages.text: Probability of Obtaining the Roots in a Quadratic Equation by Throwing a Die Three Times
negative_passages.docid: 18702
negative_passages.text: If $ax^2+(c+b)x+e+d=0$ has real roots greater than $1$, show that $ax^4+bx^3+cx^2+dx+e$ has at least one real root
negative_passages.docid: 49899
negative_passages.text: Determine the number of real roots
negative_passages.docid: 141093
negative_passages.text: How many real roots does $(x-a)^3+(x-b)^3+(x-c)^3$ have?
negative_passages.docid: 73478
negative_passages.text: Show that the equation $a_1e^{\alpha_1x} + a_2e^{\alpha_2x} + \cdots + a_ne^{\alpha_nx} = 0$ has at most $n - 1$ real roots.
negative_passages.docid: 85681
negative_passages.text: Cardinality of polynomials with real coefficients
negative_passages.docid: 38851
negative_passages.text: To find the probability whether $X$ is rational
negative_passages.docid: 130823
negative_passages.text: cubic equations which have exactly one real root
negative_passages.docid: 13656
negative_passages.text: Prove existence of a real root.
negative_passages.docid: 99502
negative_passages.text: Question on the coefficients of $(1+x+x^2+x^3+x^4)^{496}$
negative_passages.docid: 114872
negative_passages.text: If $ax^2-bx+c=0$ has two distinct real roots lying in the interval $(0,1)$ $a,b,c$ belongs to natural prove that $\log_5 {abc}\geq2$
negative_passages.docid: 86611
negative_passages.text: 2018 AMC 12A Problem 21: Which of the given polynomials has the greatest real root?
negative_passages.docid: 85065
negative_passages.text: Why can ALL quadratic equations be solved by the quadratic formula?