C
CraftExam
high importancemedium difficulty7 min

Zero product principle

If the product of two expressions is zero, then at least one of the expressions must be zero.

In one line: Zero product means zero in one bracket at least.

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Understand it

This principle is the bridge between factorised form and final roots. Once a quadratic equation is written as a product, each factor is set to zero separately.

Example

(x - 4)(x + 2) = 0 gives x = 4 or x = -2.

Formula and rule

A × B = 0 implies A = 0 or B = 0.

This is the zero product principle used after factorisation.

See it worked out

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

Worked example

For (x - 7)(x + 2) = 0, set x - 7 = 0 and x + 2 = 0.

  1. 1Then x = 7 and x = -2.
  2. 2These are the solutions because each factor separately makes the product zero.

Method you can reuse

  1. 1Write the equation in product form.
  2. 2Use the zero product principle.
  3. 3Set each factor equal to zero.
  4. 4Solve each linear equation.
  5. 5Write all roots clearly.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What should you do when (x - 7)(x + 2) = 0 appears in a question?

Think first, then show answer
Set each factor equal to zero separately. Then solve x - 7 = 0 and x + 2 = 0, because a product becomes zero only when at least one factor is zero.

Common wrong answer

Solving (x - 7)(x + 2) = 0 by saying x - 7 = x + 2 = 0 is not a proper method.

Don't mix this up

Students sometimes solve by adding the factors instead of setting each factor to zero.

Exam tip

After factorisation, never keep the product equal to zero only; split it into two separate equations.

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

The principle is often hidden inside factorisation questions and is also used in short-answer reasoning steps.
  1. 1

    Enough for 1 mark

    If the product of two expressions is zero, then at least one of the expressions must be zero.

  2. 2

    Add for 2 marks

    Example: (x - 4)(x + 2) = 0 gives x = 4 or x = -2.

  3. 3

    Add for 3 marks

    This principle is the bridge between factorised form and final roots.

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