C
CraftExam
medium importancemedium8 min

Selecting a suitable method

Selecting a suitable method means choosing factorisation, completing the square, or the quadratic formula depending on the form of the equation.

Practice This Concept

Learn the concept

Student-friendly explanation

Not every quadratic should be solved in the same way. Neat factor pairs usually suggest factorisation, while difficult coefficients often make the quadratic formula the safest choice.

How to write this in exams

  1. 1

    Start with the exact idea

    Selecting a suitable method means choosing factorisation, completing the square, or the quadratic formula depending on the form of the equation.

  2. 2

    Then show how to use it

    1. Check whether factor pairs are neat. 2. If yes, try factorisation first. 3. If not, check whether completing the square is convenient. 4. If the equation is awkward, use the quadratic formula. 5. Never waste time forcing one method.

  3. 3

    Add one concrete example

    x^2 + 11x + 24 = 0 is easy by factorisation, but 3x^2 - 2x + 7 = 0 is better handled by the formula.

  4. 4

    Avoid this incomplete answer

    Using factorisation for 3x^2 - 2x + 7 = 0 and getting stuck is a sign that the method choice was poor.

Definition

Selecting a suitable method means choosing factorisation, completing the square, or the quadratic formula depending on the form of the equation.

Example

x^2 + 11x + 24 = 0 is easy by factorisation, but 3x^2 - 2x + 7 = 0 is better handled by the formula.

Rule to remember

Use factorisation for neat integers, completing the square for form-building, and the quadratic formula for any quadratic equation.

Memory hook

Easy factors first, formula when needed.

Examples and method

Worked example

For x^2 + 11x + 24 = 0, the factors 3 and 8 work because 3 × 8 = 24 and 3 + 8 = 11. So factorisation is the fastest method. For 3x^2 - 2x + 7 = 0, no neat factor pair works quickly, so the quadratic formula is better.

Method to apply

1. Check whether factor pairs are neat. 2. If yes, try factorisation first. 3. If not, check whether completing the square is convenient. 4. If the equation is awkward, use the quadratic formula. 5. Never waste time forcing one method.

Diagram support

A method-choice box can help: neat factors, square form, or formula.

How CBSE asks it

Questions may ask students to choose the best solving method before actually solving the equation.

Avoid common mistakes

Common confusion

Students sometimes force factorisation even when the numbers are not neat and waste time.

Common wrong answer

Using factorisation for 3x^2 - 2x + 7 = 0 and getting stuck is a sign that the method choice was poor.

Exam tip

If you cannot see a clean factor pair quickly, move to the quadratic formula instead of guessing.

Quick check

Which method is usually quickest for x^2 + 11x + 24 = 0?

Factorisation is usually quickest here because 24 can be split into 3 and 8, and those numbers add to 11. The equation becomes (x + 3)(x + 8) = 0.

Answer writing and exam use

1-mark answer

Selecting a suitable method means choosing factorisation, completing the square, or the quadratic formula depending on the form of the equation.

2-mark answer

Selecting a suitable method means choosing factorisation, completing the square, or the quadratic formula depending on the form of the equation. Use factorisation for neat integers, completing the square for form-building, and the quadratic formula for any quadratic equation. x^2 + 11x + 24 = 0 is easy by factorisation, but 3x^2 - 2x + 7 = 0 is better handled by the formula.

3-mark answer

Not every quadratic should be solved in the same way. Neat factor pairs usually suggest factorisation, while difficult coefficients often make the quadratic formula the safest choice. Use factorisation for neat integers, completing the square for form-building, and the quadratic formula for any quadratic equation. For x^2 + 11x + 24 = 0, the factors 3 and 8 work because 3 × 8 = 24 and 3 + 8 = 11. So factorisation is the fastest method. For 3x^2 - 2x + 7 = 0, no neat factor pair works quickly, so the quadratic formula is better. Questions may ask students to choose the best solving method before actually solving the equation. Using factorisation for 3x^2 - 2x + 7 = 0 and getting stuck is a sign that the method choice was poor.
MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results
Practice This Concept

Help improve this page

Found something confusing, incorrect, or missing?

Practice This Concept