NCERT Mathematics, Class 10, textbook pages 10–23

How to help your child with Class 10 Maths Chapter 2, Polynomials, at home

Zeros of polynomials and their relation to coefficients, explained for parents: a 45-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

−14y = x² − 3x − 4: zeros −1 and 4

NCERT Class 10 Maths Chapter 2 Polynomials: what it teaches

Your teen reads zeros from graphs of linear and quadratic polynomials, and uses the relationships between zeros and coefficients: for ax² + bx + c, sum of zeros = −b/a and product = c/a.

Why it matters later. Polynomials lead to quadratic equations (Chapter 4) and functions in Class 11.

See it: this chapter in pictures

2x² − 8x + 6sum = −b/a = 4product = c/a = 3
Zeros relate to coefficients.
zeros 2 and −3(x − 2)(x + 3)= x² + x − 6
Work backwards from zeros.
no real zeros: misses the axis
Not every quadratic crosses the axis.

You need

  • graph paper
  • a graphing app (optional)

Tonight’s 45 minutes

  1. Graph y = x² − 3x − 4. Where does it cross the x-axis? (−1 and 4)
  2. Check: sum = 3 = −b/a, product = −4 = c/a.
  3. Build a quadratic with zeros 2 and −3: x² + x − 6.
  4. Count zeros from different graph shapes.

Words to use

  • polynomial
  • degree
  • zero
  • quadratic
  • coefficient
  • parabola

Watch for

  • Sign errors in −b/a. Write a, b, c with signs before substituting.
  • Thinking every quadratic has two zeros. A parabola may touch or miss the x-axis.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouZeros 2 and −3. The quadratic?

Your child(x − 2)(x + 3) = x² + x − 6.

A game for this week: Build a quadratic

  1. Pick two zeros.
  2. Write the quadratic.
  3. Swap and check by factorising.
  4. Points for each correct pair.

A 5-day plan, 45 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Projectile paths.
  • Profit curves.
  • Architecture arches.
  • Area problems.

Quick check

Ask these at the end of the week. Tap to see the answer.

Zeros of x² − 3x − 4?

−1 and 4.

Sum and product of zeros of 2x² − 8x + 6?

4 and 3.

Quadratic with zeros 2 and −3?

x² + x − 6.

Ready for the next chapter when your child…

  • Reads zeros from graphs.
  • Uses sum and product of zeros.
  • Forms a quadratic from zeros.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 10). See the full Class 10 parent guide for every chapter.

Questions parents ask

What is a zero of a polynomial?

A value of x that makes it 0.

How many zeros can a quadratic have?

At most two real zeros.

Is division algorithm for polynomials included?

The current syllabus focuses on zeros and coefficient relations.