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S4 Maths: Quadratic Equations and the Discriminant (Paper 2 (intermediate))
S4 Maths: Quadratic Equations and the Discriminant (Paper 2 (intermediate))
Paper 2 (intermediate): ten questions on quadratic equations and the discriminant with answers and one-line notes.
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)
- FoundationFind the discriminant of x^2 – 6x + 5 = 0 and solve it.
- FoundationIf kx^2 + 4x + 2 = 0 has equal roots, find k.
- FoundationSolve 2x^2 – 7x + 3 = 0.
- IntermediateState the sum and the product of the roots of x^2 + 2x – 8 = 0.
- IntermediateHow many distinct real roots does 3x^2 – 12x + 12 = 0 have?
- IntermediateIf x^2 + kx + 9 = 0 has a repeated root, find the possible values of k.
- ChallengeA quadratic equation has roots 2 and -5. Write down the equation.
- ChallengeThe sum of the roots is 7 and the product is 12. Find the roots.
- ChallengeSolve x^2 – 4x + 1 = 0 by the formula, correct to three decimal places.
- Error redoError clinic: what does a zero discriminant say about the number of real roots?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Discriminant = 16, x = 1 or x = 5. | The discriminant is 36 – 20 = 16, its square root is 4, and the roots are 1 and 5. |
| 2 | k = 2. | Equal roots mean a zero discriminant, so 16 – 8k = 0 and k = 2. |
| 3 | x = 3 or x = 0.5. | The discriminant is 49 – 24 = 25 with square root 5, giving 3 and 0.5. |
| 4 | Sum = -2, product = -8. | The sum is minus b over a, giving -2, and the product is c over a, giving -8. |
| 5 | One distinct real root, x = 2. | The discriminant is 144 – 144 = 0, so the two roots coincide. |
| 6 | k = 6 or k = -6. | A repeated root needs k squared minus 36 to be zero, so k is plus or minus 6. |
| 7 | x^2 + 3x – 10 = 0. | The sum is -3 and the product is -10, so the equation is x squared plus 3x minus 10. |
| 8 | 3 and 4. | They solve x^2 – 7x + 12 = 0, which factorises as (x – 3)(x – 4) = 0. |
| 9 | x = 3.732 or x = 0.268. | The discriminant is 12 with square root about 3.464, so the roots are 2 plus or minus 1.732. |
| 10 | Two equal real roots, that is one repeated root. | With a zero discriminant the two roots coincide, so the answer is two equal roots, not none. |
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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