Grade 11 Maths · Algebra

Determine the nature of roots

Use b² − 4ac to say whether the roots are real or non-real, equal or unequal, rational or irrational (for example b² − 4ac < 0 means non-real).

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The Nature of Roots of a Quadratic Equation Grade 11 MathsMiss Martins Maths and Science

Discuss the nature of Roots (using the Discriminant) - Grade 11 MathematicsMatheNatic

Nature of Roots Grade 11 Practice: Exam QuestionsMiss Martins Maths and Science

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Question 1.6 · June 2024 · Paper 1 · Provincial · 5 marks

1.6 Show that the equation

(p^{2} + 1) x^{2} = - 2 pq x - q^{2}

has no real roots for

p

and

q \in

Real numbers and

q \neq = 0

.(5)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: determine the nature of roots

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3. Question 2.3.2 · March 2023 · Paper 1 · Provincial · 2 marks
2.3 Discuss the nature of the roots of the following graphs
2.3.2 Graph showing parabola touching x-axis at one point (turning point on x-axis)(2)
Show the memo (2 ticks)Memo
1. ✓
  Roots are realThe graph touches the $x$ -axis, so the roots are real
  1 mark · Determine the nature of roots
2. ✓
  Roots are equalThe roots are equal ( $Δ = 0$ )
  1 mark · Determine the nature of roots
4. Question 1.3.2 · March 2018 · Provincial · 4 marks
1.3 Given: $f (x) = 9 x^{2} - 15 x + 4$
1.3.2 Show that $f (x) = - 3$ has no real roots.(4)
Show the memo (3 ticks)Memo
1. ✓
  Set up equation $9 x^{2} - 15 x + 4 = - 3$
  $9 x^{2} - 15 x + 7 = 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Calculate Discriminant $Δ = b^{2} - 4 a c$
  $= (- 15)^{2} - 4 (9) (7)$
  $= 225 - 252$
  $= - 27$
  2 marks · Calculate the discriminant
3. ✓
  ConclusionSince $Δ < 0$ , the equation has no real roots.
  1 mark · Determine the nature of roots

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