query: Find the number of real roots of the following equation
positive_passages.docid: 17082
positive_passages.text: Number of real roots of $2 \cos\left(\frac{x^2+x}{6}\right)=2^x+2^{-x}$
negative_passages.docid: 69618
negative_passages.text: What is the sum of non-real roots of the polynomial equation?
negative_passages.docid: 106896
negative_passages.text: Number of solutions of $x_1+2x_2+\cdots+kx_k=n$?
negative_passages.docid: 59065
negative_passages.text: Roots to an equation using analysis
negative_passages.docid: 154610
negative_passages.text: Number of solutions for the given equation in finite field of order 32.
negative_passages.docid: 112709
negative_passages.text: $\frac{1}{x-a} + \frac{1}{x-b} + \frac{1}{x-c} = 0 $ has precisely two real roots
negative_passages.docid: 69288
negative_passages.text: Number of real roots of $\sum_{k=0}^{n}\frac{x^{k}}{k!}=0$
negative_passages.docid: 18510
negative_passages.text: How to solve the following equation numerically?
negative_passages.docid: 113237
negative_passages.text: Find the sum of the roots of the floor equation
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: 47688
negative_passages.text: Number of roots of differentiable function
negative_passages.docid: 70460
negative_passages.text: How can I solve the following sequence
negative_passages.docid: 13656
negative_passages.text: Prove existence of a real root.
negative_passages.docid: 126445
negative_passages.text: Proving the second root of a quadratic equation
negative_passages.docid: 128998
negative_passages.text: Relation between real roots of a polynomial and real roots of its derivative
negative_passages.docid: 44354
negative_passages.text: Total number of solutions of an equation
negative_passages.docid: 157710
negative_passages.text: $x^{3}-x-2=0$ how do I find the roots?