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Formulas exist for finding the roots of third- and fourth-degree polynomials.

the verdict
SUPPORTED
the evidence backs this
Recorded sources
6 sources for · 0 against

Counts group repeated records of the same source within each side. They do not measure evidence strength or source independence.

Is it true that formulas exist for finding the roots of third- and fourth-degree polynomials?

Yes. Multiple reliable mathematical sources confirm that algebraic formulas exist for finding the exact roots of both third-degree (cubic) and fourth-degree (quartic) polynomials.

Verdict: SUPPORTED · 6 sources for, 0 against · Last checked

How claims like this are judged

Judged against reference works: claims of this kind are settled by the historical reference record, not journal abstracts.

Evidence for · 6
Wikipedia: Cubic equation
Reference article covering this claim directly
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Wikipedia: Cubic equation. (n.d.). Wikipedia. https://en.wikipedia.org/wiki/Cubic_equation

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More for · 5
Wikipedia: Quartic equation
Reference article covering this claim directly
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Wikipedia: Quartic equation. (n.d.). Wikipedia. https://en.wikipedia.org/wiki/Quartic_equation

LibreTexts: LibreTexts: 14.7.06: Newtons Method
Explicitly states that formulas exist for third- and fourth-degree polynomials.
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LibreTexts: LibreTexts: 14.7.06%3A Newtons Method. (n.d.). LibreTexts. https://eng.libretexts.org/Bookshelves/Introductory_Engineering/EGR_1010%3A_Introduction_to_Engineering_for_Engineers_and_Scientists/14%3A_Fundamentals_of_Engineering/14.07%3A_Infinitesimal_calculus_for_derivatives/14.7.06%3A_Newtons_Method

OpenStax: OpenStax Calculus Volume 1: 4.9 Newton’s Method
Affirms that formulas exist for third- and fourth-degree polynomials.
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OpenStax: OpenStax Calculus Volume 1: 4.9 Newton’s Method. (n.d.). OpenStax. https://openstax.org/books/calculus-volume-1/pages/c0e46c4d-3d5c-400e-a3b9-af3cb3e066e2@

Semantic Scholar peS2o: Annular Bounds for the Zeros of a Polynomial
States that for polynomials of third and fourth degree, there are analogous formulas to find the zeros.
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Semantic Scholar peS2o: Annular Bounds for the Zeros of a Polynomial. (n.d.). Semantic Scholar peS2o. http://downloads.hindawi.com/journals/ijmms/2018/6047387.pdf

Wikipedia: Wikipedia: Polynomial root-finding
Notes that closed-form formulas for polynomial roots exist when the degree is less than 5, including cubic and quartic.
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Wikipedia: Wikipedia: Polynomial root-finding. (n.d.). Wikipedia. https://en.wikipedia.org/wiki/Polynomial_root-finding

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