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  2. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    This formula can be straightforwardly transformed into a formula for the roots of a general cubic equation, using the back-substitution described in § Depressed cubic. The formula can be proved as follows: Starting from the equation t 3 + pt + q = 0, let us set t = u cos θ.

  3. Casus irreducibilis - Wikipedia

    en.wikipedia.org/wiki/Casus_irreducibilis

    Casus irreducibilis (from Latin 'the irreducible case') is the name given by mathematicians of the 16th century to cubic equations that cannot be solved in terms of real radicals, that is to those equations such that the computation of the solutions cannot be reduced to the computation of square and cube roots. Cardano's formula for solution in ...

  4. Quartic function - Wikipedia

    en.wikipedia.org/wiki/Quartic_function

    For a general formula that is always true, one thus needs to choose a root of the cubic equation such that m ≠ 0. This is always possible except for the depressed equation y 4 = 0. Now, if m is a root of the cubic equation such that m ≠ 0, equation becomes

  5. Quartic equation - Wikipedia

    en.wikipedia.org/wiki/Quartic_equation

    There exists a general formula for finding the roots to quartic equations, provided the coefficient of the leading term is non-zero. However, since the general method is quite complex and susceptible to errors in execution, it is better to apply one of the special cases listed below if possible.

  6. Polynomial transformation - Wikipedia

    en.wikipedia.org/wiki/Polynomial_transformation

    This already suffices to solve the quadratic by square roots. In the case of the cubic, Tschirnhaus transformations replace the variable by a quadratic function, thereby making it possible to eliminate two terms, and so can be used to eliminate the linear term in a depressed cubic to achieve the solution of the cubic by a combination of square ...

  7. Shoppers in their 50s and 60s say Eva Longoria's $10 root ...

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    L'Oreal Paris Magic Root Cover Up is available in nine shades (as opposed to the three that most brands offer) and works to conceal gray hairs until your next shampoo. With over 45,000 five-star ...

  8. Resolvent cubic - Wikipedia

    en.wikipedia.org/wiki/Resolvent_cubic

    The polynomial P(x) has a rational root (this can be determined using the rational root theorem). The resolvent cubic R 3 (y) has a root of the form α 2, for some non-null rational number α (again, this can be determined using the rational root theorem). The number a 2 2 − 4a 0 is the square of a rational number and a 1 = 0. Indeed:

  9. Eva Longoria Uses This $9 Magic Root Spray to Cover Gray Hair ...

    www.aol.com/entertainment/eva-longoria-uses-9...

    Aging is inevitable, but you can still cover up unwanted color with the help of hair products. And thanks to a tip from Eva Longoria, we just discovered a $9 solution!