Grade 11 · Theory
Nature and sum of roots
Quadratics · about 3 min
Visual overview: Nature and sum of roots1 MIN READ
2 study sections · pause after each one and recall the key ideaBeyond finding roots, Grade 11 asks you to reason about them algebraically.
Key points- Sum of roots = −b/a; product of roots = c/a.
- These let you build a quadratic from its roots: x² − (sum)x + (product) = 0.
- Combined with the discriminant, they answer "nature of roots" questions fully.
- Always state whether roots are real, equal, rational or irrational.
- Nature of roots — a description (real/non-real, equal/unequal, rational/irrational).
EXAM TIP
nature-of-roots answers need BOTH the calculation of Δ and a sentence interpreting it.