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2. Cubic function - Wikipedia

   en.wikipedia.org/wiki/Cubic_function

   If b 2 – 3ac = 0, then there is only one critical point, which is an inflection point. If b 2 – 3ac < 0, then there are no (real) critical points. In the two latter cases, that is, if b 2 – 3ac is nonpositive, the cubic function is strictly monotonic. See the figure for an example of the case Δ 0 > 0.

3. Quadratic formula - Wikipedia

   en.wikipedia.org/wiki/Quadratic_formula

   The roots of the quadratic function y = ⁠ 1 / 2 ⁠ x 2 − 3x + ⁠ 5 / 2 ⁠ are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.

4. Pythagorean triple - Wikipedia

   en.wikipedia.org/wiki/Pythagorean_triple

   Animation demonstrating the smallest Pythagorean triple, 3 2 + 4 2 = 5 2. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2. Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.

5. Equation solving - Wikipedia

   en.wikipedia.org/wiki/Equation_solving

   An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign.

6. List of theorems - Wikipedia

   en.wikipedia.org/wiki/List_of_theorems

   Fuchs's theorem (differential equations) Fuglede's theorem (functional analysis) Full employment theorem (theoretical computer science) Fulton–Hansen connectedness theorem (algebraic geometry) Fundamental theorem of algebra (complex analysis) Fundamental theorem of arbitrage-free pricing (financial mathematics)

7. Complex conjugate root theorem - Wikipedia

   en.wikipedia.org/wiki/Complex_conjugate_root_theorem

   In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P. [1]