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Identifying a Quadratic Equation

A quadratic equation is any equation that can be simplified to ax2 + bx + c = 0 with a ≠ 0.

In one line: Degree 2 only, not degree 1 or 3.

Practice This Concept

Understand it

Not every equation with x is quadratic. To identify a quadratic equation, first simplify it and check that the highest power of x is 2 and no higher power remains.

Example

2x(x - 3) = 8 becomes 2x2 - 6x - 8 = 0, so it is quadratic.

Formula and rule

After simplification, the equation must have the form ax2 + bx + c = 0, with a ≠ 0 and no term of degree higher than 2.

See it worked out

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

Worked example

Take 2x(x - 3) = 8.

  1. 1Expanding gives 2x2 - 6x = 8.
  2. 2Bringing 8 to the left gives 2x2 - 6x - 8 = 0.
  3. 3Since the highest power is 2, the equation is quadratic.

Method you can reuse

  1. 1Expand brackets or remove fractions if needed.
  2. 2Bring all terms to one side.
  3. 3Check the highest power of x.
  4. 4If the highest power is 2, it is quadratic.

Visual tip

A quick flow chart is useful: simplify first, check highest power, then classify the equation.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is 2x(x - 3) = 8 a quadratic equation after simplification?

Think first, then show answer
Because expanding gives 2x2 - 6x - 8 = 0, and the highest power of x is 2. That is exactly the condition for a quadratic equation.

Common wrong answer

Saying 3x + 5 = 0 is quadratic.

Why it loses marks: The highest power is only 1.

Don't mix this up

Students sometimes call any equation with x a quadratic equation, even when the highest power is 1 or 3.

Exam tip

Always simplify first. The equation is quadratic only if the highest power after simplification is exactly 2.

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 whether a given relation is quadratic after expansion or simplification.
  1. 1

    Enough for 1 mark

    A quadratic equation is any equation that can be simplified to ax2 + bx + c = 0 with a ≠ 0.

  2. 2

    Add for 2 marks

    Example: 2x(x - 3) = 8 becomes 2x2 - 6x - 8 = 0, so it is quadratic.

  3. 3

    Add for 3 marks

    To identify a quadratic equation, first simplify it and check that the highest power of x is 2 and no higher power remains.

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