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Solving Quadratics by Factorising | Mathematics for GCSE/IGCSE - Year 11 PDF Download
How do I solve a quadratic equation using factorisation?
- Rearrange the expression into the form ax2 + bx + c = 0, ensuring zero is on one side. It's preferable to use the side where 𝑎a is positive.
- Factorize the quadratic equation and solve each bracket by setting it equal to zero. For instance, if (x + 4)(x − 1) = 0, then either x + 4 = 0 or x − 1 = 0, as when A × B = 0, either A = 0 or B = 0.
- To solve (x − 3)(x + 7) = 0:
- Solve "first bracket = 0": x − 3 = 0, so x = 3.
- Solve "second bracket = 0": x + 7 = 0, giving x = −7.
- Thus, the solutions are x = 3 or x = −7, with the solutions having opposite signs to the numbers in the brackets.
- To solve (2x − 3)(3x + 5) = 0:
- Solve "first bracket = 0": 2x − 3 = 0, leading to x = 3/2.
- Solve "second bracket = 0": 3x + 5 = 0, yielding x =
. - Hence, the solutions are
- To solve x(x − 4) = 0:
- Think of x as (x − 0) or x.
- Solve "first bracket = 0": x = 0.
- Solve "second bracket = 0": x − 4 = 0, which gives x=4.
- Therefore, the solutions are x = 0 or x = 4.
- Avoid dividing both sides by x initially, as it can lead to a loss of solutions (in this case, x = 0).
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FAQs on Solving Quadratics by Factorising - Mathematics for GCSE/IGCSE - Year 11
| 1. Can you explain the process of solving a quadratic equation by factorisation? |  |
| 2. What are some tips for factorising quadratic equations effectively? | |
Ans. One tip for factorising quadratic equations is to look for common factors and factor them out first. Another tip is to consider using the AC method, where you find two numbers that multiply to give ac and add up to give b. Practice and familiarity with different factorisation techniques can also improve your efficiency in solving quadratics.
| 3. Are there any common mistakes to avoid when factorising quadratic equations? | |
Ans. One common mistake to avoid is forgetting to check if the factors you obtain actually multiply back to the original quadratic expression. Additionally, make sure to always check for common factors that can be factored out before attempting to factorise the quadratic further.
| 4. How can I check my solutions after factorising a quadratic equation? | |
Ans. After factorising a quadratic equation and finding the solutions, you can substitute these solutions back into the original equation to verify if they satisfy the equation and make it true. This step ensures that the solutions obtained through factorisation are correct.
| 5. Can all quadratic equations be solved by factorisation? | |
Ans. Not all quadratic equations can be solved by factorisation, especially if the equation cannot be easily factored into linear factors. In such cases, other methods like the quadratic formula or completing the square may be more suitable for finding the solutions.
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Apr 13, 2025
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