An Exercise on Quadratic Equations – 3 Solution Methods: Factorization + Completing Square + Formula

Published: 2026-09-11 Categories: Equations and Identities Editor: MathSir Difficulty: ★★★☆☆ Reading time: ~16 minutes Pageview: 32

Synopsis

Quadratic equations are a core topic in DSE Mathematics, appearing in both Paper 1 Section A(1) and A(2). This article covers the three essential solution methods: factorization, completing the square, and the quadratic formula. You will learn how to choose the most appropriate method for each equation, step-by-step techniques, and how to avoid common mistakes. Worked examples, DSE exam tips, practice questions, and homework are all included to build your confidence and speed.

Article

Click the following link to read the original article with a title：
 Quadratic Equations – 3 Solution Methods: Factorization + Completing Square + Formula

Exercise

Solve each equation using the most efficient method.

  1. \(x^2 - 25 = 0\)
  2. \(x^2 + 2x - 8 = 0\)
  3. \(3x^2 - 10x + 3 = 0\)
  4. \(x^2 - 6x + 2 = 0\)
  5. \(2x^2 + 4x - 1 = 0\)
  6. \(x^2 - 5x - 1 = 0\)
  7. \(4x^2 - 12x + 9 = 0\)
  8. \(x^2 + 7x + 12 = 0\)
  9. \(2x^2 - 3x - 5 = 0\)
  10. \(x^2 - 4x - 7 = 0\)

Exercise

1. \(x = \pm 5\)
2. \(x = 2 \text{ or } -4\)
3. \(x = 3 \text{ or } \frac{1}{3}\)
4. \(x = 3 \pm \sqrt{7}\)
5. \(x = \frac{-2 \pm \sqrt{6}}{2}\)
6. \(x = \frac{5 \pm \sqrt{29}}{2}\)
7. \(x = \frac{3}{2}\) (repeated)
8. \(x = -3 \text{ or } -4\)
9. \(x = \frac{5}{2} \text{ or } -1\)
10. \(x = 2 \pm \sqrt{11}\)

Keywords

 We simplify the tough stuff, so you can ace your DSE Maths.

DSE Maths Categories

DSE Maths Tags

Who is MathSir ?

MathSir (Colin Chan) serves as the editor and webmaster of this website. For further information about him, you are welcome to visit his personal page ( mathsir.cc ).


DSE Mathematics

Friendly Links