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Common errors in quadratic formula substitution

These are mistakes made while substituting a, b, and c into the quadratic formula, especially sign mistakes and denominator mistakes.

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Student-friendly explanation

The formula is reliable only when the values are copied correctly. Many wrong answers come from writing b with the wrong sign, forgetting ±, or using 2 instead of 2a.

How to write this in exams

  1. 1

    Start with the exact idea

    These are mistakes made while substituting a, b, and c into the quadratic formula, especially sign mistakes and denominator mistakes.

  2. 2

    Then show how to use it

    1. Write a, b, c separately. 2. Keep the signs exactly as given. 3. Calculate D carefully. 4. Use 2a in the denominator. 5. Write both roots or state if roots are not real.

  3. 3

    Add one concrete example

    For 2x^2 - 4x + 3 = 0, the denominator must be 2a = 4, not just 2.

  4. 4

    Avoid this incomplete answer

    Using b = 4 for 2x^2 - 4x + 3 = 0 is wrong because the minus sign belongs to b.

Definition

These are mistakes made while substituting a, b, and c into the quadratic formula, especially sign mistakes and denominator mistakes.

Example

For 2x^2 - 4x + 3 = 0, the denominator must be 2a = 4, not just 2.

Rule to remember

Use x = (-b ± √(b^2 - 4ac)) / 2a. Remember: b keeps its sign, and the denominator is 2a.

Memory hook

Copy signs as they are, then solve.

Examples and method

Worked example

For 2x^2 - 4x + 3 = 0, a = 2, b = -4, c = 3. So x = (4 ± √(16 - 24)) / 4. The denominator is 4 because 2a = 4. Here the discriminant is negative, so there are no real roots.

Method to apply

1. Write a, b, c separately. 2. Keep the signs exactly as given. 3. Calculate D carefully. 4. Use 2a in the denominator. 5. Write both roots or state if roots are not real.

Diagram support

A labelled substitution box for a, b, c, D, and denominator is very helpful.

How CBSE asks it

CBSE often frames a solution and asks students to find the exact substitution error or the final root.

Avoid common mistakes

Common confusion

Students often change b from -4 to +4 or forget that the denominator depends on a.

Common wrong answer

Using b = 4 for 2x^2 - 4x + 3 = 0 is wrong because the minus sign belongs to b.

Exam tip

Write a, b, and c separately before starting the formula; do not substitute in a hurry.

Quick check

In x^2 - 6x + 5 = 0, what is the most common substitution mistake?

The common mistake is writing b = 6 instead of b = -6. The sign of b must stay the same as it appears in the equation.

Answer writing and exam use

1-mark answer

These are mistakes made while substituting a, b, and c into the quadratic formula, especially sign mistakes and denominator mistakes.

2-mark answer

These are mistakes made while substituting a, b, and c into the quadratic formula, especially sign mistakes and denominator mistakes. Use x = (-b ± √(b^2 - 4ac)) / 2a. Remember: b keeps its sign, and the denominator is 2a. For 2x^2 - 4x + 3 = 0, the denominator must be 2a = 4, not just 2.

3-mark answer

The formula is reliable only when the values are copied correctly. Many wrong answers come from writing b with the wrong sign, forgetting ±, or using 2 instead of 2a. Use x = (-b ± √(b^2 - 4ac)) / 2a. Remember: b keeps its sign, and the denominator is 2a. For 2x^2 - 4x + 3 = 0, a = 2, b = -4, c = 3. So x = (4 ± √(16 - 24)) / 4. The denominator is 4 because 2a = 4. Here the discriminant is negative, so there are no real roots. CBSE often frames a solution and asks students to find the exact substitution error or the final root. Using b = 4 for 2x^2 - 4x + 3 = 0 is wrong because the minus sign belongs to b.
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