enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    A cubic equation with real coefficients can be solved geometrically using compass, straightedge, and an angle trisector if and only if it has three real roots. [30]: Thm. 1 A cubic equation can be solved by compass-and-straightedge construction (without trisector) if and only if it has a rational root.

  3. Cubic function - Wikipedia

    en.wikipedia.org/wiki/Cubic_function

    The derivative of a cubic function is a quadratic function. A cubic function with real coefficients has either one or three real roots (which may not be distinct); [1] all odd-degree polynomials with real coefficients have at least one real root. The graph of a cubic function always has a single inflection point.

  4. Cube root - Wikipedia

    en.wikipedia.org/wiki/Cube_root

    Cubic equations, which are polynomial equations of the third degree (meaning the highest power of the unknown is 3) can always be solved for their three solutions in terms of cube roots and square roots (although simpler expressions only in terms of square roots exist for all three solutions, if at least one of them is a rational number).

  5. Geometrical properties of polynomial roots - Wikipedia

    en.wikipedia.org/wiki/Geometrical_properties_of...

    Writing the equation as ... d 2 is the positive root of the cubic equation () ... The root separation of a polynomial is the minimal distance between two roots, ...

  6. Cubic equations of state - Wikipedia

    en.wikipedia.org/wiki/Cubic_equations_of_state

    This equation may have up to three roots. The maximal root of the cubic equation generally corresponds to a vapor state, while the minimal root is for a liquid state. This should be kept in mind when using cubic equations in calculations, e.g., of vapor-liquid equilibrium.

  7. Nested radical - Wikipedia

    en.wikipedia.org/wiki/Nested_radical

    The nested radicals in this solution cannot in general be simplified unless the cubic equation has at least one rational solution. Indeed, if the cubic has three irrational but real solutions, we have the casus irreducibilis, in which all three real solutions are written in terms of cube roots of complex numbers. On the other hand, consider the ...

  8. 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 being real numbers, then its complex conjugate a − bi is also a root of P.

  9. Vieta's formulas - Wikipedia

    en.wikipedia.org/wiki/Vieta's_formulas

    Vieta's formulas can be proved by considering the equality + + + + = () (which is true since ,, …, are all the roots of this polynomial), expanding the products in the right-hand side, and equating the coefficients of each power of between the two members of the equation.