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S4 Maths: Quadratic Equations and the Discriminant (Paper 4 (error clinic))

S4 Maths: Quadratic Equations and the Discriminant (Paper 4 (error clinic))

  • 2026-11-15

Tutor Prep Guide · Solving quadratic equations by factorising and by the formula, the sign of the discriminant, the sum and product of roots, forming an equation from given roots, and finding the range of a parameter

S4 Maths: Quadratic Equations and the Discriminant (Paper 4 (error clinic))

Paper 4 (error clinic): ten questions on quadratic equations and the discriminant with answers and one-line notes.

Direct answers　Level: S4 maths; format: factorising, the quadratic formula, the discriminant, sum and product of roots.

01　Paper details (check answers afterwards)

Item Detail
Questions 10
Suggested time 20
Difficulty mix Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter Chapter: S4 Maths: Quadratic Equations and the Discriminant
Level S4

02　Questions (10 items)

  1. FoundationSolve x^2 – 9 = 0.
  2. FoundationFind the discriminant of x^2 + 6x + 9 = 0 and state the repeated root.
  3. FoundationSolve x^2 – x – 6 = 0.
  4. IntermediateFind the discriminant of 2x^2 – 4x + 5 = 0 and state the number of real roots.
  5. IntermediateState the sum and product of the roots of x^2 – 5x + 4 = 0.
  6. IntermediateIf kx^2 – 6x + 3 = 0 has a repeated root, find k.
  7. ChallengeThe roots are 2 and 7. Write down the equation.
  8. ChallengeIf x^2 + 4x + k = 0 has two distinct real roots, find the range of k.
  9. ChallengeThe sum of the roots is 5 and the product is 6. Find the roots.
  10. Error redoError clinic: when b is negative, how is b squared evaluated?

03　Answers and one-line notes

# Answer One-line note
1 x = 3 or x = -3. Rearranging gives x squared equal to 9, and the square root has two signs.
2 Discriminant = 0, repeated root x = -3. The discriminant is 36 – 36 = 0, and -6 divided by 2 gives -3.
3 x = 3 or x = -2. Factorising gives (x – 3)(x + 2) = 0, so the roots are 3 and -2.
4 Discriminant = -24, so no real roots. The discriminant is 16 – 40 = -24, which is negative, so there is no real root.
5 Sum = 5, product = 4. The roots are 1 and 4, giving sum 5 and product 4, matching the formulas.
6 k = 3. A zero discriminant gives 36 – 12k = 0, so k = 3.
7 x^2 – 9x + 14 = 0. The sum is 9 and the product 14, so the equation is x squared minus 9x plus 14.
8 k < 4. Distinct real roots need 16 – 4k > 0, so k is less than 4.
9 2 and 3. The equation is x^2 – 5x + 6 = 0, which factorises as (x – 2)(x – 3) = 0.
10 Square the sign as well, so for b = -3 we get 9. A square is always positive, and dropping the minus sign ruins the discriminant.

04　What to do after marking

  • After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
  • Repeat the same item two days later; move to the next paper only when both attempts are correct.
  • Parents only need the answer and note columns; there is no need to explain every item.

Write down a, b and c first, then work out the discriminant. A positive discriminant gives two distinct real roots, a zero discriminant one repeated root, and a negative one no real root. For a parameter question, form the discriminant in terms of the parameter and then set it positive, zero or negative.Tutor Registration →

Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.

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