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The discriminant b^2 - 4ac determines the number of real roots.

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 the discriminant b^2 - 4ac determines the number of real roots?

Yes. Multiple algebra references state that the discriminant b^2-4ac determines the number and nature of the real roots of a quadratic equation, with its sign distinguishing two real, one repeated, or no real roots.

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

The private library was unavailable for some searches in this check. Missing library results are not evidence against the claim.

Evidence for · 6
Discriminant
Get citation
Discriminant. (n.d.). en.wikipedia.org. https://en.wikipedia.org/wiki/Discriminant

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More for · 5
The Number of Real Roots of a Cubic Equation
2008
Get citation
Richard, K. & B., T. J. (2008). The Number of Real Roots of a Cubic Equation. eric.ed.gov. https://eric.ed.gov/?id=EJ875531

Edexcel Maths A level Year 1 (And AS) All-in-One Complete Revision and Practice: For the 2020 Autumn & 2021 Summer Exams (Collins A level Revision)
2020
Get citation
A-level, C. (2020). Edexcel Maths A level Year 1 (And AS) All-in-One Complete Revision and Practice: For the 2020 Autumn & 2021 Summer Exams (Collins A level Revision). books.google.com. http://books.google.com/books?id=auAEEAAAQBAJ&dq=The+discriminant+b%5E2+-+4ac+determines+the+number+of+real+roots.&hl=&as_pt=BOOKS&source=gbs_api

QUADRATIC EQUATIONS: THEORY, DISCRIMINANT AND SOLUTION METHODS
2026
Get citation
Toshbo'lov, O. (2026). QUADRATIC EQUATIONS: THEORY, DISCRIMINANT AND SOLUTION METHODS. zenodo.org. https://doi.org/10.5281/zenodo.18487420

Explorations in College Algebra
2000
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Kime, L. A. & Clark, J. (2000). Explorations in College Algebra. books.google.com. http://books.google.com/books?id=NhdIdC1SI6QC&dq=The+discriminant+b%5E2+-+4ac+determines+the+number+of+real+roots.&hl=&as_pt=BOOKS&source=gbs_api

Precalculus
2014
Get citation
Kolman, B. & Shapiro, A. (2014). Precalculus. play.google.com. https://play.google.com/store/books/details?id=nLPiBQAAQBAJ&source=gbs_api

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