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When to Solve by Factorisation
- Factorisation is used when the question specifically asks to solve by factorisation.
- For example:
- Part (a): Factorise 6x2 - 7x - 3
- Part (b): Solve 6x2 - 7x - 3 = 0
- Factorisation is also employed when dealing with two-term quadratic equations.
- For instance:
- Solving x2 - 4x = 0 by taking out a common factor of x to obtain x(x - 4) = 0, resulting in x = 0 and x = 4
- Solving x2 - 9 = 0 by using the difference of two squares to factorise it as (x + 3)(x - 3) = 0, giving x = -3 and x = 3 (Alternatively, rearranging to x2 = 9 and using ±√ to get x = ±3)
When should I use the quadratic formula?
- When solving for equations that require solutions accurate to a given precision such as 2 decimal places or 3 significant figures.
- When the quadratic formula proves to be a faster method compared to factorization.
- For instance, when dealing with equations like 36x2 - 33x - 20 = 0.
- If uncertain about which method to use, resorting to the quadratic formula is a reliable approach as it always provides solutions.
When should I solve by completing the square?
- When part (a) of a question says to complete the square and part (b) says to use part (a) to solve the equation
- When making x the subject of harder formulae containing x2 and x terms
- For example, make x the subject of the formula x2 + 6x = y
- Complete the square: (x + 3)2 – 9 = y
- Add 9 to both sides: (x + 3)2 = y + 9
- Take square roots and use ±:
- Subtract 3:
- For example, make x the subject of the formula x2 + 6x = y
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FAQs on Quadratic Equation Methods - Mathematics for GCSE/IGCSE - Class 10
| 1. What is the Quadratic Formula and how is it used to solve quadratic equations? |  |
Ans. The Quadratic Formula is used to find the roots of a quadratic equation in the form ax^2 + bx + c = 0. The formula is x = (-b ± √(b^2 - 4ac)) / 2a. By substituting the values of a, b, and c into the formula, we can calculate the roots of the quadratic equation.
| 2. How can Completing the Square be used to solve quadratic equations? | |
Ans. Completing the Square is a method used to solve quadratic equations by transforming the equation into a perfect square trinomial. By adding and subtracting a constant term to make the quadratic expression a perfect square, we can easily find the roots of the equation.
| 3. What is the Factorization Technique for solving quadratic equations? | |
Ans. The Factorization Technique involves factoring the quadratic equation into two binomial factors. By finding the factors of the quadratic equation that multiply to the constant term and add up to the coefficient of the middle term, we can easily solve the equation.
| 4. When should we use the Quadratic Formula instead of other methods to solve quadratic equations? | |
Ans. The Quadratic Formula is most useful when the quadratic equation cannot be easily factored or when the roots are irrational or complex numbers. In such cases, the Quadratic Formula provides an efficient way to find the roots of the equation.
| 5. Which method is the most efficient for solving quadratic equations - Completing the Square, Factorization, or the Quadratic Formula? | |
Ans. The efficiency of each method depends on the complexity of the quadratic equation. Completing the Square is useful for perfect square trinomials, Factorization works well for easily factorable equations, while the Quadratic Formula is a general method that can be used for any quadratic equation.
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Sep 30, 2025
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