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Verification of obtained roots

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

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

Example

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

Rule to remember

Verification means testing each root in the original equation. A correct root must make the left side equal zero.

Memory hook

Root first, replace next, zero last.

Examples and method

Worked example

If x = 2 is found from x^2 - 5x + 6 = 0, substitute it: 2^2 - 5(2) + 6 = 4 - 10 + 6 = 0. The same happens for x = 3. So both roots are correct.

Method to apply

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

Diagram support

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

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.

Avoid common mistakes

Common confusion

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

Common wrong answer

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

Exam tip

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

Quick check

Why should roots be checked after solving a quadratic equation?

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.

Answer writing and exam use

1-mark answer

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

2-mark answer

Verification means substituting the obtained roots back into the original quadratic equation to check whether they really satisfy it. Verification means testing each root in the original equation. A correct root must make the left side equal zero. For x^2 - 5x + 6 = 0, check x = 2 and x = 3 by substitution.

3-mark answer

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. Verification means testing each root in the original equation. A correct root must make the left side equal zero. If x = 2 is found from x^2 - 5x + 6 = 0, substitute it: 2^2 - 5(2) + 6 = 4 - 10 + 6 = 0. The same happens for x = 3. So both roots are correct. Students may be asked to verify a claimed root, or a final answer may need a check as part of the solution. Checking only the factorised form and not the original equation can hide earlier algebra errors.
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