Grade 11 Maths · Algebra

Use the discriminant to find k

Find the values of an unknown constant k that give the kind of roots asked for (for example real roots need b² − 4ac ≥ 0).

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Nature of the roots Grade11: L2 Find a value for kOnline Maths by Miss Pythagoras

Find the Value of K for which the Quadratic has Equal Roots - Quick and Simple ExplanationPreMath

Find the Value of k in Quadratics for Different Scenarios Involving Roots | Step-by-Step ExplanationPreMath

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Question 1.3 · March 2025 · Paper 1 · Provincial · 2 marks

1.3 The roots of a quadratic equation are

x = \frac{- 3 \pm 13 - 2 k}{4}

. Calculate the values of

k

for which the root(s) are equal.(2)

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

More past paper questions: use the discriminant to find k

Work each one out first, then open the memo and check every tick.

3. Question 1.5.2 · June 2024 · Paper 1 · Provincial · 2 marks
1.5 For which values of $p$ will $- 2 x^{2} + 4 x - 3 = - p$ :
1.5.2 have roots that are BOTH positive?(2)
Show the memo (2 ticks)Memo
1. ✓
  Analyze conditions for positive rootsFrom 1.5.1, we have roots if $p > 1$ .
  For positive roots, $c > 0$ (since $a > 0$ and $b < 0$ ).
  $3 - p > 0$
  $- p > - 3$
  $p < 3$
  1 mark · Use the discriminant to find k
2. ✓
  Combine conditions $1 < p < 3$
  1 mark · Use the discriminant to find k
4. Question 1.3.2 · March 2023 · Paper 1 · Provincial · 2 marks
1.3 Given a quadratic equation $3 x^{2} + 7 x + \frac{11 h}{12} = 0$ .
1.3.2 Determine the largest integral value of h for which the roots will be rational.(2)
Show the memo (2 ticks)Memo
1. ✓
  Analyze discriminant for integer values of hFor rational roots, $Δ$ must be a perfect square.
  Try $h = 4$ : $Δ = 49 - 11 (4) = 5$ (Not square)
  Try $h = 3$ : $Δ = 49 - 11 (3) = 16$ (Perfect square)
  1 mark · Use the discriminant to find k
2. ✓
  State the answer $h = 3$
  1 mark · Use the discriminant to find k
5. Question 1.3.1 · March 2021 · Paper 1 · Provincial · 3 marks
1.3 Given: $k x^{2} - 5 x - 1 = 0$ , with $k \neq = 0$ .
1.3.1 For which value(s) of k will $k x^{2} - 5 x - 1 = 0$ have real roots?(3)
Show the memo (2 ticks)Memo
1. ✓
  Determine discriminant condition $Δ \geq 0$
  $b^{2} - 4 a c \geq 0$
  $(- 5)^{2} - 4 (k) (- 1) \geq 0$
  2 marks · Use the discriminant to find k
2. ✓
  Solve inequality $25 + 4 k \geq 0$
  $4 k \geq - 25$
  $k \geq - \frac{25}{4}$ (or $k \geq - 6, 25$ )
  1 mark · Use the discriminant to find k
6. Question 2.4.1 · March 2015 · Provincial · 2 marks
2.4 Roots of equations
2.4.1 The roots of a quadratic equation are: $x = \frac{2 \pm m + 6}{2}$ . For which values of m are the roots unreal?(2)
Show the memo (2 ticks)Memo
1. ✓
  Condition for unreal roots $m + 6 < 0$
  1 mark · Use the discriminant to find k
2. ✓
  Solve inequality $m < - 6$
  1 mark · Use the discriminant to find k

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