query: Understanding the term "double roots" of a quadratic equation
positive_passages.docid: 157417
positive_passages.text: Understanding the definition of a multiple (double) root
negative_passages.docid: 81669
negative_passages.text: The logic of the AC Method of factoring quadratic polynomials
negative_passages.docid: 44296
negative_passages.text: Solving a cubic polynomial equation.
negative_passages.docid: 33184
negative_passages.text: Something strange about $\sqrt{ 4+ \sqrt{ 4 + \sqrt{ 4-x}}}=x$ and its friends
negative_passages.docid: 103165
negative_passages.text: the number of the positive integer numbers $k$ that makes for the two quadratic equations $ \pm x^2 \pm px \pm k$ rational roots.
negative_passages.docid: 154393
negative_passages.text: Roots of polynomial with real coefficients appear in conjugate pairs.
negative_passages.docid: 158063
negative_passages.text: A formula for the roots of a solvable polynomial
negative_passages.docid: 109304
negative_passages.text: The roots of the equation $z^n=(1+z)^n$...
negative_passages.docid: 153480
negative_passages.text: Roots of a characteristic equation. Can Mathematica solve it?
negative_passages.docid: 150624
negative_passages.text: Why does the square root of a square involve the plus-minus sign?
negative_passages.docid: 135774
negative_passages.text: Alternating roots of $f(x) = \exp(x) \sin(x) -1$ and $\exp(x)\cos(x) +1$
negative_passages.docid: 77820
negative_passages.text: Roots in a polynomial ring
negative_passages.docid: 74626
negative_passages.text: Rate of convergence of Newton's method near a double root.
negative_passages.docid: 134927
negative_passages.text: How can a square root be defined since it has two answers?
negative_passages.docid: 61548
negative_passages.text: What would be the roots of the derivative of this polynomial
negative_passages.docid: 148074
negative_passages.text: Analytic expression for the primitive of square root of a quadratic
negative_passages.docid: 121373
negative_passages.text: Elementary Symmetric Polynomials, Roots of cubic polynomials