# The Nature of the Roots

> This section classifies the roots of ax^2+bx+c=0 using the discriminant Δ=b^2-4ac. Δ is the expression under the square root on the information-sheet formula: determine the nature of the roots does…

- Page: https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/the-nature-of-the-roots

Breadcrumbs: [Home](https://www.hlayiso.com/) › [Grade 12](https://www.hlayiso.com/grade-12) › [Mathematics](https://www.hlayiso.com/grade-12/mathematics) › [Notes](https://www.hlayiso.com/grade-12/mathematics/notes) › [Algebraic expressions, equations and inequalities](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities) › [The Nature of the Roots](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/the-nature-of-the-roots)

## Full notes

This is a preview of the The Nature of the Roots notes for Grade 12 Mathematics. Create a free Hlayiso account to read the full notes, practise every question and track your progress.

## More in Algebraic expressions, equations and inequalities

- [Simultaneous Equations](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/simultaneous-equations) — Previous section
- [All Algebraic expressions, equations and inequalities sections](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities)

## Frequently asked questions

### What will I learn in "The Nature of the Roots"?

This section covers The Nature of the Roots as part of Algebraic expressions, equations and inequalities in Grade 12 Mathematics. You'll find clear explanations, worked examples, and key definitions aligned to the CAPS curriculum.

### Is this section aligned with the CAPS curriculum?

Yes. All notes on Hlayiso, including "The Nature of the Roots", are written against the official CAPS curriculum and ATP for Grade 12 Mathematics.

### What should I study after "The Nature of the Roots"?

Continue with the next section in Algebraic expressions, equations and inequalities, or test your understanding with the interactive quiz linked to this section.

---

Hlayiso: free CAPS and IEB past papers, memos, notes and study guides for South African learners. When citing, link the page URL above, not a PDF or /api/ URL.