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Standard form and coefficients

The standard form of a quadratic equation is ax2 + bx + c = 0, where a, b, and c are coefficients and a ≠ 0.

In one line: a sits with x2, b sits with x, c stands alone.

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Understand it

To work correctly with quadratic equations, students must first write them in standard form. After that, the values of a, b, and c can be read directly, including their signs.

Example

In 5x2 - 2x + 9 = 0, a = 5, b = -2, and c = 9.

Formula and rule

Standard form is ax2 + bx + c = 0 with a ≠ 0.

If a term is missing, its coefficient is 0, but the x2 term must still be present.

See it worked out

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

Worked example

For 3x2 - 7x + 2 = 0, compare term by term with ax2 + bx + c = 0.

  1. 1So a = 3, b = -7, and c = 2.
  2. 2These values are then used in factorisation, completing the square, or the quadratic formula.

Method you can reuse

  1. 1Write the equation as ax2 + bx + c = 0.
  2. 2Check the x2 term first to get a.
  3. 3Check the x term to get b, with sign.
  4. 4Check the constant term to get c.
  5. 5Use these values only after the equation is in standard form.

Visual tip

A small coefficient table works well: x2 term, x term, constant term, with a, b, c written below them.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What are a, b, and c in x2 + 7x - 8 = 0?

Think first, then show answer
Here a = 1, b = 7, and c = -8. The coefficient of x2 is 1 even when it is not written, and the sign of the constant term must be kept exactly as given.

Common wrong answer

Writing b = 2 for 3x2 - 2x + 9 = 0.

Why it loses marks: The coefficient of x is -2, not 2.

Don't mix this up

Students often forget that the sign of b or c belongs to the coefficient, not just the number written after it.

Exam tip

Always compare the given equation term by term with ax2 + bx + c = 0 before using any formula.

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 identify coefficients, rewrite an equation in standard form, or use the right values in the quadratic formula.
  1. 1

    Enough for 1 mark

    The standard form of a quadratic equation is ax2 + bx + c = 0, where a, b, and c are coefficients and a ≠ 0.

  2. 2

    Add for 2 marks

    Example: In 5x2 - 2x + 9 = 0, a = 5, b = -2, and c = 9.

  3. 3

    Add for 3 marks

    After that, the values of a, b, and c can be read directly, including their signs.

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