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Quartics

is an option for functions that involve solving algebraic equations that specifies whether explicit forms for solutions to quartic equations should be given.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
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Quartics

Quartics

is an option for functions that involve solving algebraic equations that specifies whether explicit forms for solutions to quartic equations should be given.

Details

  • With Quartics->True, roots of quartics are given explicitly in terms of radicals. With Quartics->False, roots of quartics that do not have very simple forms are given implicitly in terms of Root objects.
  • Quartics->True may lead to fairly large outputs.

Examples

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Basic Examples  (1)

By default Reduce does not use the general formulas for solving quartics in radicals:

With Quartics->True, Reduce solves all quartics in terms of radicals:

Solving this simple quartic in radicals does not require the general formulas:

Scope  (2)

By default Eigenvalues does not use the general formulas for solving quartics in radicals:

With Quartics->True all quartics are solved in terms of radicals:

By default ToRadicals converts all quartic Root objects to radicals:

With Quartics->False, ToRadicals does not use the general formulas for solving quartics:

Wolfram Research (1988), Quartics, Wolfram Language function, https://reference.wolfram.com/language/ref/Quartics.html.

Text

Wolfram Research (1988), Quartics, Wolfram Language function, https://reference.wolfram.com/language/ref/Quartics.html.

CMS

Wolfram Language. 1988. "Quartics." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Quartics.html.

APA

Wolfram Language. (1988). Quartics. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Quartics.html

BibTeX

@misc{reference.wolfram_2025_quartics, author="Wolfram Research", title="{Quartics}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Quartics.html}", note=[Accessed: 08-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_quartics, organization={Wolfram Research}, title={Quartics}, year={1988}, url={https://reference.wolfram.com/language/ref/Quartics.html}, note=[Accessed: 08-August-2025]}