What is a quadratic equation and how is it different from a linear equation in Class 10 Maths?

A quadratic equation is any equation of the form ax² + bx + c = 0, where the highest power of the variable is 2. A linear equation has only x (power 1) and gives one solution; a quadratic equation has x² and gives two solutions called roots. In CBSE Class 10 Chapter 4, students learn three methods to find these roots — factorisation, completing the square, and the quadratic formula.

What are the three methods to solve quadratic equations in CBSE Class 10 and which one is easiest?

The three CBSE-prescribed methods are: factorisation (fastest when factors are visible), completing the square (conceptually important but slow), and the quadratic formula — x = (−b ± √(b²−4ac)) / 2a (most reliable for all cases). For board exams, factorisation saves time on simple equations; the quadratic formula is the safest fallback when factorisation is not obvious. Most CBSE toppers default to factorisation first, formula second.

What is the discriminant in quadratic equations and why does CBSE Class 10 always ask about it?

The discriminant is D = b² − 4ac, the expression inside the square root of the quadratic formula. It determines the nature of roots without solving the equation: if D > 0, two distinct real roots; if D = 0, two equal real roots; if D < 0, no real roots. CBSE board papers consistently carry a 1–2 mark question asking students to find the nature of roots — making the discriminant one of the highest-certainty marks available in Chapter 4.

How many marks does Chapter 4 Quadratic Equations carry in CBSE Class 10 Maths board exam and what type of questions are asked?

Quadratic Equations typically carries 10–12 marks in CBSE Class 10 Maths board papers. Question types include: 1-mark MCQs on discriminant and nature of roots, 2-mark solve-by-factorisation problems, 3-mark word problems requiring equation formation, and 4-mark completing-the-square or formula-based questions. Word problems — where a real-life situation must be converted into a quadratic equation — are the most commonly dropped marks and require the most focused practice.

My Class 10 child can solve quadratic equations in practice but makes mistakes in the actual exam — what is going wrong?

This is a sign-and-calculation error pattern, not a concept gap. In quadratic equations, the most common exam mistakes are: wrong sign when applying the formula (especially with negative b), arithmetic errors inside the square root, and failing to check whether both roots satisfy the original equation in word problems. These errors do not appear in relaxed practice but surface under timed exam pressure. The fix is timed mock drills — not more concept revision.

Is it true that the quadratic formula always works for every quadratic equation in Class 10 CBSE Maths?

Yes, the quadratic formula works for every quadratic equation — but it is not always the fastest method, and it does not always produce real roots. When D < 0, the formula gives no real solution, which is a valid answer for CBSE Class 10 (real roots do not exist). Students lose marks by either applying factorisation to equations that cannot be factorised easily, or by forgetting to check D before attempting the formula. Always calculate D first — it takes 10 seconds and saves minutes.

📘 Chapter GuideClass 10CBSE · NCERT Aligned

Quadratic Equations Class 10: How to Score Full Marks

Q: How many marks does Chapter 4 Quadratic Equations carry in CBSE Class 10 Maths board exam and what type of questions are asked?

Quadratic Equations typically carries 10–12 marks in CBSE Class 10 Maths board papers. Question types include: 1-mark MCQs on discriminant and nature of roots, 2-mark solve-by-factorisation problems, 3-mark word problems requiring equation formation, and 4-mark completing-the-square or formula-based questions. Word problems — where a real-life situation must be converted into a quadratic equation — are the most commonly dropped marks and require the most focused practice.

Q: My Class 10 child can solve quadratic equations in practice but makes mistakes in the actual exam — what is going wrong?

This is a sign-and-calculation error pattern, not a concept gap. In quadratic equations, the most common exam mistakes are: wrong sign when applying the formula (especially with negative b), arithmetic errors inside the square root, and failing to check whether both roots satisfy the original equation in word problems. These errors do not appear in relaxed practice but surface under timed exam pressure. The fix is timed mock drills — not more concept revision.

Q: Is it true that the quadratic formula always works for every quadratic equation in Class 10 CBSE Maths?

Yes, the quadratic formula works for every quadratic equation — but it is not always the fastest method, and it does not always produce real roots. When D < 0, the formula gives no real solution, which is a valid answer for CBSE Class 10 (real roots do not exist). Students lose marks by either applying factorisation to equations that cannot be factorised easily, or by forgetting to check D before attempting the formula. Always calculate D first — it takes 10 seconds and saves minutes.

By The Classmate AI Editorial Team·5 min read·Updated 23 September 2026

✓ CBSE Class 10 · NCERT-aligned

⚡ Quick Answer

In the current rationalised CBSE Class 10 syllabus, quadratic equations are solved by two methods: factorisation (fastest when the equation splits cleanly into two linear factors) and the quadratic formula (works on every quadratic). Solving by completing the square is no longer in the syllabus. Most marks are lost not by choosing the wrong method but through sign errors when substituting a, b and c, skipped working steps, and not rejecting roots that make no sense in word problems.

Quadratic Equations is a chapter in the Algebra unit of CBSE Class 10 Maths, and it shows up every year — usually as a short "solve" or "nature of roots" question plus a word problem. Most students lose marks here not because they pick the wrong method, but because they drop a sign, skip a step, or forget to reject a root that makes no sense.

Here's how to avoid those losses.

Syllabus check first: in the current rationalised NCERT/CBSE syllabus, you solve quadratic equations by factorisation and by the quadratic formula. Solving by completing the square was removed from the syllabus, so don't spend revision time on it (more on that below).

Method 1 — Factorisation

The fastest method when the equation factorises cleanly.

Factorisation works when you can break the quadratic into two linear factors. For example, x² + 5x + 6 = 0 factors as (x + 2)(x + 3) = 0, giving roots x = -2 and x = -3.

The quick spotting check: when the coefficient of x² is 1, look for two numbers that multiply to give the constant term and add to give the coefficient of x. If you find them quickly, factorise. If not, go straight to Method 2 instead of guessing.

When the coefficient of x² is not 1, split the middle term: multiply a × c, find two numbers that multiply to ac and add to b, and split bx using them. For 2x² - 5x + 3 = 0: ac = 6, and –2 and –3 multiply to 6 and add to –5, so 2x² - 2x - 3x + 3 = 0 → 2x(x - 1) - 3(x - 1) = 0 → (2x - 3)(x - 1) = 0, giving x = 3/2 or x = 1.

Another example: x² - 7x + 12 = 0. The two numbers are –3 and –4 (they multiply to 12 and add to –7), so it factors as (x - 3)(x - 4) = 0.

Method 2 — Quadratic Formula

The safety net. It works on every quadratic, as long as you substitute carefully.

The formula is: x = [-b ± √(b² - 4ac)] / 2a

For ax² + bx + c = 0, you must identify a, b, and c correctly — including their signs. This is the step where marks are most often lost.

The common mistake: writing b = 5 when the equation is 2x² - 5x + 3 = 0. The correct values are a = 2, b = -5, and c = 3. Notice b is negative, so -b = 5.

Working it through: x = [5 ± √(25 - 24)] / 4 = [5 ± 1] / 4, so x = 1.5 or x = 1 — the same roots factorisation gave above, which is a useful way to check your work.

Always rewrite the equation in standard form ax² + bx + c = 0 before you identify the coefficients. If the question gives 3x² = 2x + 5, first rearrange it to 3x² - 2x - 5 = 0.

What about completing the square?

Completing the square is where the quadratic formula comes from, and you'll meet it again in Class 11. But solving by completing the square is not part of the current rationalised CBSE Class 10 syllabus, so it isn't a method you need to prepare for this exam. If you have spare time, it's worth understanding; if you're short on time, factorisation and the formula are enough.

Word Problems — The 3-Step Framework

Most quadratic word problems reduce to the same 3 steps. Once you see them, speed problems and area problems feel identical.

Step 1: Identify the unknown. Let it be x, and write every other quantity in terms of x.

Step 2: Translate the English into an equation using the given information, then rearrange it into standard form.

Step 3: Solve using Method 1 or Method 2. Discard any root that doesn't make sense (for example, a negative length or a negative speed), and say why you're discarding it — that sentence is part of a complete answer.

Example: "A rectangular garden is 4 m longer than it is wide. Its area is 96 m². Find its dimensions."

Let width = x m. Then length = x + 4 m.
Area: x(x + 4) = 96 → x² + 4x - 96 = 0
Factorise: (x + 12)(x - 8) = 0 → x = -12 or x = 8
Since width cannot be negative, x = 8 m and length = 12 m.
Check: 8 × 12 = 96 ✓

Discriminant — What Examiners Are Testing

When the question says "find the nature of the roots", it's testing one thing: do you know what b² - 4ac tells you?

The discriminant D = b² - 4ac determines:

If D > 0: two distinct real roots
If D = 0: two equal real roots
If D < 0: no real roots

A common variation asks for the value of k for which an equation has equal roots. Set D = 0 and solve for k. For kx² - 6x + 1 = 0: D = 36 - 4k = 0, so k = 9.

Practical takeaway: before solving any quadratic, compute the discriminant. It tells you whether real roots exist and whether they're equal, which is also a quick check on your final answer.

Practise the chapter

For a full set of practice questions on this chapter, each with a model answer, see our CBSE Class 10 Maths Quadratic Equations important questions. Work through them on paper first, then check your method against the answer.

Trigonometry Class 10 CBSE: Understand Every Formula in 1 Hour — the same derive-don't-memorise approach, for trigonometry
CBSE Class 10 Maths Exam Preparation Guide — how every chapter on this blog fits into one revision plan

Ready to try it yourself? Practice CBSE Class 8–10 Maths and Science with step-by-step AI tutoring — start a free session on Classmate AI.

Frequently asked questions

What is a quadratic equation and how is it different from a linear equation in Class 10 Maths?
A quadratic equation is any equation of the form ax² + bx + c = 0, where the highest power of the variable is 2. A linear equation has only x (power 1) and gives one solution; a quadratic equation has x² and gives two solutions called roots. In CBSE Class 10 Chapter 4, students learn three methods to find these roots — factorisation, completing the square, and the quadratic formula.
What are the three methods to solve quadratic equations in CBSE Class 10 and which one is easiest?
The three CBSE-prescribed methods are: factorisation (fastest when factors are visible), completing the square (conceptually important but slow), and the quadratic formula — x = (−b ± √(b²−4ac)) / 2a (most reliable for all cases). For board exams, factorisation saves time on simple equations; the quadratic formula is the safest fallback when factorisation is not obvious. Most CBSE toppers default to factorisation first, formula second.
What is the discriminant in quadratic equations and why does CBSE Class 10 always ask about it?
The discriminant is D = b² − 4ac, the expression inside the square root of the quadratic formula. It determines the nature of roots without solving the equation: if D > 0, two distinct real roots; if D = 0, two equal real roots; if D < 0, no real roots. CBSE board papers consistently carry a 1–2 mark question asking students to find the nature of roots — making the discriminant one of the highest-certainty marks available in Chapter 4.
How many marks does Chapter 4 Quadratic Equations carry in CBSE Class 10 Maths board exam and what type of questions are asked?
Quadratic Equations typically carries 10–12 marks in CBSE Class 10 Maths board papers. Question types include: 1-mark MCQs on discriminant and nature of roots, 2-mark solve-by-factorisation problems, 3-mark word problems requiring equation formation, and 4-mark completing-the-square or formula-based questions. Word problems — where a real-life situation must be converted into a quadratic equation — are the most commonly dropped marks and require the most focused practice.
My Class 10 child can solve quadratic equations in practice but makes mistakes in the actual exam — what is going wrong?
This is a sign-and-calculation error pattern, not a concept gap. In quadratic equations, the most common exam mistakes are: wrong sign when applying the formula (especially with negative b), arithmetic errors inside the square root, and failing to check whether both roots satisfy the original equation in word problems. These errors do not appear in relaxed practice but surface under timed exam pressure. The fix is timed mock drills — not more concept revision.
Is it true that the quadratic formula always works for every quadratic equation in Class 10 CBSE Maths?
Yes, the quadratic formula works for every quadratic equation — but it is not always the fastest method, and it does not always produce real roots. When D < 0, the formula gives no real solution, which is a valid answer for CBSE Class 10 (real roots do not exist). Students lose marks by either applying factorisation to equations that cannot be factorised easily, or by forgetting to check D before attempting the formula. Always calculate D first — it takes 10 seconds and saves minutes.