medium importancemedium difficulty8 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.

In one line: Easy factors first, formula when needed.

Practice This Concept

Understand it

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.

Example

x² + 11x + 24 = 0 is easy by factorisation, but 3x² - 2x + 7 = 0 is better handled by the formula.

Formula and rule

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

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

For x² + 11x + 24 = 0, the factors 3 and 8 work because 3 × 8 = 24 and 3 + 8 = 11.

1So factorisation is the fastest method.
2For 3x² - 2x + 7 = 0, no neat factor pair works quickly, so the quadratic formula is better.

Method you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Which method is usually quickest for x² + 11x + 24 = 0?

Think first, then show answer

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.

Common wrong answer

Using factorisation for 3x² - 2x + 7 = 0 and getting stuck is a sign that the method choice was poor.

Don't mix this up

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

Exam tip

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

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

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

1
Enough for 1 mark
Selecting a suitable method means choosing factorisation, completing the square, or the quadratic formula depending on the form of the equation.
2
Add for 2 marks
Example: x² + 11x + 24 = 0 is easy by factorisation, but 3x² - 2x + 7 = 0 is better handled by the formula.
3
Add for 3 marks
Not every quadratic should be solved in the same way.

MCQ Quiz

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