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2. Radical (chemistry) - Wikipedia

   en.wikipedia.org/wiki/Radical_(chemistry)

   Lewis dot structure of a Hydroxide ion compared to a hydroxyl radical. In chemistry, a radical, also known as a free radical, is an atom, molecule, or ion that has at least one unpaired valence electron. [ 1][ 2] With some exceptions, these unpaired electrons make radicals highly chemically reactive. Many radicals spontaneously dimerize.

3. Free-radical reaction - Wikipedia

   en.wikipedia.org/wiki/Free-radical_reaction

   A free-radical reaction is any chemical reaction involving free radicals. This reaction type is abundant in organic reactions. Two pioneering studies into free radical reactions have been the discovery of the triphenylmethyl radical by Moses Gomberg (1900) and the lead-mirror experiment[ 1] described by Friedrich Paneth in 1927.

4. Solution in radicals - Wikipedia

   en.wikipedia.org/wiki/Solution_in_radicals

   Solution in radicals. A solution in radicals or algebraic solution is a closed-form expression, and more specifically a closed-form algebraic expression, that is the solution of a polynomial equation, and relies only on addition, subtraction, multiplication, division, raising to integer powers, and the extraction of n th roots (square roots ...

5. Quartic equation - Wikipedia

   en.wikipedia.org/wiki/Quartic_equation

   In mathematics, a quartic equation is one which can be expressed as a quartic function equaling zero. The general form of a quartic equation is. Graph of a polynomial function of degree 4, with its 4 roots and 3 critical points. where a ≠ 0. The quartic is the highest order polynomial equation that can be solved by radicals in the general ...

6. Cubic equation - Wikipedia

   en.wikipedia.org/wiki/Cubic_equation

   Cubic equation. Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis at y = 0 ). The case shown has two critical points. Here the function is and therefore the three real roots are 2, -1 and -4. In algebra, a cubic equation in one variable is an equation of the form in which a is not zero.

7. Abel–Ruffini theorem - Wikipedia

   en.wikipedia.org/wiki/Abel–Ruffini_theorem

   Abel–Ruffini theorem. In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Here, general means that the coefficients of the equation are viewed and manipulated as indeterminates .

8. Free-radical addition - Wikipedia

   en.wikipedia.org/wiki/Free-radical_addition

   In organic chemistry, free-radical addition is an addition reaction which involves free radicals. Radical additions are known for a variety of unsaturated substrates, both olefinic or aromatic and with or without heteroatoms. Free-radical reactions depend on one or more relatively weak bonds in a reagent. Under reaction conditions (typically ...

9. Nested radical - Wikipedia

   en.wikipedia.org/wiki/Nested_radical

   Nested radical. In algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression. Examples include. which arises in discussing the regular pentagon, and more complicated ones such as.