← Lesson📄 Worksheet✅ Memo📝 Exam test🗝️ Marking guide
∑ DANEMATHICS
FREE CAPS MATHS RESOURCES
Grade 11 · Equations
The Discriminant & Nature of Roots: Full Guide
WORKSHEET
Name: 
Class: 
Date: 
Mark
  / 20

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    Δ for x2 − 6x + 9 = 0, and the nature of roots. (classify)
    (2)
  2. 2
    Δ for x2 + 2x + 5 = 0, and the nature of roots. (classify)
    (2)
  3. 3
    Δ for 2x2 − 7x + 3 = 0, and the nature. (classify)
    (2)
  4. 4
    Are the roots of x2 − 4x + 4 = 0 rational? (rational?)
    (2)
  5. 5
    Rational or irrational: x2 − 2x − 2 = 0? (rational?)
    (2)
  6. 6
    For which k does x2 + kx + 4 = 0 have equal roots? (equal, find k)
    (2)
  7. 7
    For which k does x2 − 6x + k = 0 have equal roots? (equal, find k)
    (2)
  8. 8
    For which k does x2 + 2x + k = 0 have two real roots? (real, find k)
    (2)
  9. 9
    For which k does x2 − 2x + k = 0 have no real roots? (non-real, find k)
    (2)
  10. 10
    Δ for 3x2 − 5x + 1 = 0. (compute)
    (2)
TOTAL: 20 marks
© Danemathics — free to print and share for classroom use.danemathics.com

Printing this sheet

  1. In the print dialog open More settings and untick “Headers and footers” — that is what prints the date, time and web address in the margin.
  2. Leave Pages per sheet on 1 so learners keep the full writing space.
  3. Choose Save as PDF as the destination to download it instead of printing.