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The Cubic Formula Roots of the General Cubic Equation
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Why is it that, unlike with the quadratic formula, nobody teaches the cubic formula? After all, they do lots of polynomial torturing in schools and the discovery of the cubic formula is considered to be one of the milestones in the history of mathematics. It's all a bit of a mystery and our mission today is to break through this mathematical wall of silence! Lots of cubic (and at the very end quartic) surprises ahead. • The Cubic Formula: Roots of the General Cubic Equation • In algebra, a cubic equation in one variable is an equation of the form • ax^3+bx^2+cx+d=0 • in which a is nonzero. • The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). All of the roots of the cubic equation can be found by the following means: • Algebraically, that is, they can be expressed by a cubic formula involving the four coefficients, the four basic arithmetic operations and nth roots (radicals). (This is also true of quadratic (second-degree) and quartic (fourth-degree) equations, but not of higher-degree equations, by the Abel–Ruffini theorem.) • Trigonometrically • Numerical approximations of the roots can be found using root-finding algorithms such as Newton's method. • The coefficients do not need to be real numbers. Much of what is covered below is valid for coefficients in any field with characteristic other than 2 and 3. The solutions of the cubic equation do not necessarily belong to the same field as the coefficients. For example, some cubic equations with rational coefficients have roots that are irrational (and even non-real) complex numbers. • #Derivation #Cubic #Equation • Watch the video and Learn Something Extraordinary... • Subscribe: BRAIN EXPLODERS • Link: / brainexploders • A challenge for you in the last of this videos of the playlist Exploders Contest, can you solve that questions? Watch the videos, Take your time give your answer in the comment section, if your answer is correct, we'll announce your name in our next YouTube video of this playlist - Exploders Contest: Season 2. • Season 2 Link: • Marvel Way to Find An Angle - 95% Get... • Suggested Book: • Title: Cubic Equation Solver - Solve cubic equations easily! • Link: https://amzn.to/2CVajTL • Exploders Contest: Season 1 • Link: • EXPLODERS CONTEST: Season 1 • This is the channel to feature this type of questions suggested by the people. • Join us on another platforms • Instagram: / brain_exploders • Facebook: / brainexploders • Messenger: https://www.m.me/brainexploders • Twitter: / brainexploders • Telegram: https://t.me/Brain_Exploders • ___Show your support to us. • ________THANKS FOR WATCHING • #Brain_Exploders • _______________Next video will come soon.
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