query: How to prove that the equation $x^5-1102x^4-2015x=0$ has at least three real roots?
positive_passages.docid: 153816
positive_passages.text: Real Roots and Differentiation
negative_passages.docid: 5410
negative_passages.text: Prove that $a^2 + b^2 \geq 8$ if $ x^4 + ax^3 + 2x^2 + bx + 1 = 0 $ has at least one real root.
negative_passages.docid: 29876
negative_passages.text: Find the number of triples $(x,y,z)$ of real numbers satisfying the equation $x^4+y^4+z^4+1=4xyz$
negative_passages.docid: 22058
negative_passages.text: Prove that $\cos(\pi/7)$ is root of equation $8x^3-4x^2-4x+1=0$
negative_passages.docid: 103246
negative_passages.text: Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)
negative_passages.docid: 18911
negative_passages.text: Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)
negative_passages.docid: 90612
negative_passages.text: Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots
negative_passages.docid: 137048
negative_passages.text: If $p, q, r$ are the roots of $x^3 -x+1=0$, what is $p^5 + q^5 + r^5$?
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 $b+c\neq 4$
negative_passages.docid: 61148
negative_passages.text: Finding real roots of $ P(x)=x^8 - x^7 +x^2 -x +15$
negative_passages.docid: 140481
negative_passages.text: How to tell if a quartic equation has a multiple root.
negative_passages.docid: 116277
negative_passages.text: real values of $x$ in $\sqrt{5-x} = 5-x^2$.
negative_passages.docid: 43470
negative_passages.text: Prove: For odd integers $a$ and $b$, the equation $x^2 + 2 a x + 2 b = 0$ has no integer or rational roots.
negative_passages.docid: 156034
negative_passages.text: sufficient condition for a polynomial to have roots in $[0,1]$
negative_passages.docid: 33010
negative_passages.text: Roots of $ x^{13} - e^{-x} + x - sin(x) = 0$
negative_passages.docid: 38662
negative_passages.text: If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$
negative_passages.docid: 114379
negative_passages.text: Show that number of solutions satisfying $x^5=e$ is a multiple of 4?