medium importancemedium difficulty7 min

Verification of obtained roots

Verification means substituting the obtained roots back into the original quadratic equation to check whether they really satisfy it.

In one line: Root first, replace next, zero last.

Practice This Concept

Understand it

Even a small sign mistake can produce a wrong root, so checking is important. Verification builds confidence and helps catch hidden errors before final submission.

Example

For x² - 5x + 6 = 0, check x = 2 and x = 3 by substitution.

Formula and rule

Verification means testing each root in the original equation.

A correct root must make the left side equal zero.

See it worked out

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

Worked example

If x = 2 is found from x² - 5x + 6 = 0, substitute it: 2² - 5(2) + 6 = 4 - 10 + 6 = 0.

1The same happens for x = 3.
2So both roots are correct.

Method you can reuse

1Take one root.
2Substitute it into the original equation.
3Simplify carefully.
4See whether the result is zero.
5Repeat for the other root.

Visual tip

A simple check table with root, substitution, and result zero or not zero is useful.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why should roots be checked after solving a quadratic equation?

Think first, then show answer

They should be checked to make sure no sign or factorisation mistake happened while solving. Substitution tells us whether each root really makes the original equation true.

Common wrong answer

Checking only the factorised form and not the original equation can hide earlier algebra errors.

Don't mix this up

Students often verify against the transformed equation instead of the original one.

Exam tip

When asked to verify, always substitute into the original equation, not into an already simplified version only.

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

Students may be asked to verify a claimed root, or a final answer may need a check as part of the solution.

1
Enough for 1 mark
Verification means substituting the obtained roots back into the original quadratic equation to check whether they really satisfy it.
2
Add for 2 marks
Example: For x² - 5x + 6 = 0, check x = 2 and x = 3 by substitution.
3
Add for 3 marks
Even a small sign mistake can produce a wrong root, so checking is important.

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