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  2. 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.

  3. Hurwitz polynomial - Wikipedia

    en.wikipedia.org/wiki/Hurwitz_polynomial

    where, if the discriminant b 24ac is less than zero, then the polynomial will have two complex-conjugate solutions with real part −b/2a, which is negative for positive a and b. If the discriminant is equal to zero, there will be two coinciding real solutions at −b/2a.

  4. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    Because (a + 1) 2 = a, a + 1 is the unique solution of the quadratic equation x 2 + a = 0. On the other hand, the polynomial x 2 + ax + 1 is irreducible over F 4, but it splits over F 16, where it has the two roots ab and ab + a, where b is a root of x 2 + x + a in F 16. This is a special case of Artin–Schreier theory.

  5. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    Graph of y = ax 2 + bx + c, where a and the discriminant b 24ac are positive, with. Roots and y-intercept in red; Vertex and axis of symmetry in blue; Focus and directrix in pink; Visualisation of the complex roots of y = ax 2 + bx + c: the parabola is rotated 180° about its vertex (orange).

  6. Sharp EL-5120 - Wikipedia

    en.wikipedia.org/wiki/Sharp_EL-5120

    The Sharp EL-5120 is a scientific programmable calculator. It has about 1 KB of total RAM available to the user, and has 4 basic operational modes: Real mode: it is the basic operational mode for directly performing standard algebraic and statistical calculations, as well as evaluating user-defined functions and numerically integrating them.

  7. Solving quadratic equations with continued fractions - Wikipedia

    en.wikipedia.org/wiki/Solving_quadratic...

    By the fundamental theorem of algebra, if the monic polynomial equation x 2 + bx + c = 0 has complex coefficients, it must have two (not necessarily distinct) complex roots. Unfortunately, the discriminant b 2 − 4c is not as useful in this situation, because it may be a complex number. Still, a modified version of the general theorem can be ...

  8. Quadratic integral - Wikipedia

    en.wikipedia.org/wiki/Quadratic_integral

    Assume that the discriminant q = b 24ac is positive. In that case, define u and A by = +, and = = (). The quadratic integral can now ...

  9. Elementary algebra - Wikipedia

    en.wikipedia.org/wiki/Elementary_algebra

    Yet the above logic is still valid to show that if abc = 0 then a = 0 or b = 0 or c = 0 if, instead of letting a = a and b = bc, one substitutes a for a and b for bc (and with bc = 0, substituting b for a and c for b). This shows that substituting for the terms in a statement isn't always the same as letting the terms from the statement equal ...