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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.

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Basic Examples  
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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:

Wolfram Language code: Reduce[x ^ 4 + 2 x ^ 2 + 3 x + 4 == 0, x]//Last

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

Wolfram Language code: Reduce[x ^ 4 + 2 x ^ 2 + 3 x + 4 == 0, x, Quartics -> True]//Last

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

Wolfram Language code: Reduce[x ^ 4 - 5 == 0, x]

Scope  (2)

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

Wolfram Language code: Eigenvalues[{{1, 2, 1, 4}, {2, 1, 2, 2}, {3, 2, 1, 2}, {1, 3, 2, 1}}, 1]

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

Wolfram Language code: Eigenvalues[{{1, 2, 1, 4}, {2, 1, 2, 2}, {3, 2, 1, 2}, {1, 3, 2, 1}}, 1, Quartics -> True]

By default ToRadicals converts all quartic Root objects to radicals:

Wolfram Language code: nums = {Root[# ^ 4 - 12# + 7&, 1], Root[# ^ 4 - 5&, 1]}
Wolfram Language code: ToRadicals[nums]

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

Wolfram Language code: ToRadicals[nums, Quartics -> False]
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_2026_quartics, author="Wolfram Research", title="{Quartics}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Quartics.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_quartics, organization={Wolfram Research}, title={Quartics}, year={1988}, url={https://reference.wolfram.com/language/ref/Quartics.html}, note=[Accessed: 13-June-2026]}