query: Finding the sum of non-unique roots of cubic equations
positive_passages.docid: 157975
positive_passages.text: If $\alpha^3 - 3\alpha^2 + 5\alpha -17 =0 $ and $\beta^3 - 3\beta^2 + 5\beta+11 =0 $ then find value of $\alpha+\beta$($\alpha,\beta$ is real number)
negative_passages.docid: 155012
negative_passages.text: Solving quadratic equations in modular arithmetic
negative_passages.docid: 137109
negative_passages.text: Evaluating a summation of inverse squares over odd indices
negative_passages.docid: 106716
negative_passages.text: The sum of square roots of non-perfect squares is never integer
negative_passages.docid: 31076
negative_passages.text: Roots of unity filter, identity involving $\sum_{k \ge 0} \binom{n}{3k}$
negative_passages.docid: 31977
negative_passages.text: How to prove sum of powers property of roots of unity?
negative_passages.docid: 138756
negative_passages.text: How to Calculate the Sum of Coefficients in a Polynomial with known Integer Roots
negative_passages.docid: 74452
negative_passages.text: On a uniqueness proof for solutions of $\ a + x = b\,$ in a group
negative_passages.docid: 31200
negative_passages.text: Convert from Nested Square Roots to Sum of Square Roots
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: 1519
negative_passages.text: Sum of derivatives of a polynomial
negative_passages.docid: 64448
negative_passages.text: Find a quadratic equation with root $x_1^2$ and $x_2^2$
negative_passages.docid: 116360
negative_passages.text: Sum of n-th roots of unity
negative_passages.docid: 110416
negative_passages.text: Sums of roots of unity
negative_passages.docid: 78379
negative_passages.text: Proof on cubic residues
negative_passages.docid: 134311
negative_passages.text: How to determine equation for $\sum_{k=1}^n k^3$
negative_passages.docid: 18519
negative_passages.text: About multi-root search in Mathematica for transcendental equations