medium importancemedium difficulty7 min

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.

In one line: Copy signs as they are, then solve.

Practice This Concept

Understand it

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.

Example

For 2x² - 4x + 3 = 0, the denominator must be 2a = 4, not just 2.

Formula and rule

Use x = (-b ± √(b² - 4ac)) / 2a.

Remember: b keeps its sign, and the denominator is 2a.

See it worked out

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

Worked example

For 2x² - 4x + 3 = 0, a = 2, b = -4, c = 3.

1So x = (4 ± √(16 - 24)) / 4.
2The denominator is 4 because 2a = 4.
3Here the discriminant is negative, so there are no real roots.

Method you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

In x² - 6x + 5 = 0, what is the most common substitution mistake?

Think first, then show answer

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.

Common wrong answer

Using b = 4 for 2x² - 4x + 3 = 0.

Why it loses marks: The minus sign belongs to b.

Don't mix this up

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

Exam tip

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

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

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

1
Enough for 1 mark
These are mistakes made while substituting a, b, and c into the quadratic formula, especially sign mistakes and denominator mistakes.
2
Add for 2 marks
Example: For 2x² - 4x + 3 = 0, the denominator must be 2a = 4, not just 2.
3
Add for 3 marks
The formula is reliable only when the values are copied correctly.

MCQ Quiz

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