Quadratic Equations — Class 10 Maths MCQ with Answers (2026-27)

Updated · checked against the CBSE 2026-27 syllabus

13 objective questions on Quadratic Equations, every one checked against the CBSE 2026-27 syllabus. Pick an option and the correct answer is shown straight away, with your marks running at the top. A new question opens each day until all 13 are unlocked.

What the 2026-27 syllabus covers in Quadratic Equations

Quadratic Equations MCQ questions with answers

  1. If the roots of the quadratic polynomial are equal, where the​ discriminant‌ D = b² − 4ac, then
    1. D > 0
    2. D < 0
    3. D ≥ 0
    4. D = 0

    Answer: d) D = 0

    The discriminant measures how many times the curve meets the x-axis. Equal roots means it just touches, which happens exactly when b² − 4ac = 0.

  2. Raj's car travels at a speed of x km/h while Ajay's car‌ travels‌ 5 km/h faster than Raj's car. Raj took 4 hours more than Ajay to complete the journey of 400 km. What will be the distance covered by Ajay's car in two hours?
    1. 2(x + 5) km
    2. (x − 5) km
    3. 2(x + 10) km
    4. (2x + 5) km

    Answer: a) 2(x + 5) km

    Ajay's speed is 5 km/h more than Raj's, so it is (x + 5) km/h. In 2 hours he covers 2(x + 5) km.

  3. Which of the​ following​ quadratic equations describes the speed of Raj's car?
    1. x² − 5x − 500 = 0
    2. x² + 4x − 400 = 0
    3. x² + 5x − 500 = 0
    4. x² − 4x + 400 = 0

    Answer: c) x² + 5x − 500 = 0

    Times are 400/x and 400/(x+5), differing by 4 hours. So 400(x+5) − 400x = 4x(x+5), which simplifies to x² + 5x − 500 = 0.

  4. What is the speed‌ of​ Raj's car?
    1. 20 km/h
    2. 15 km/h
    3. 25 km/h
    4. 10 km/h

    Answer: a) 20 km/h

    Factorise x² + 5x − 500 = (x + 25)(x − 20). Speed cannot be negative, so x = 20 km/h.

  5. How much time did Ajay​ take‌ to travel 400 km?
    1. 20 hours
    2. 40 hours
    3. 25 hours
    4. 16 hours

    Answer: d) 16 hours

    Ajay drives at 20 + 5 = 25 km/h, so his time is 400 ÷ 25 = 16 hours.

  6. The speed of a motor boat is 20 km/hr. For covering a distance of 15 km the boat took 1 hour more upstream than downstream. Let the​ speed​ of the stream be x km/hr. Then the speed of the motorboat upstream will be
    1. 20 km/hr
    2. (20 + x) km/hr
    3. (20 − x) km/hr
    4. 2 km/hr

    Answer: c) (20 − x) km/hr

    Going upstream the current works against the boat, so the speeds subtract: (20 − x) km/hr.

  7. Which is the correct quadratic​ equation‌ for the speed of the current?
    1. x² + 30x − 200 = 0
    2. x² + 20x − 400 = 0
    3. x² + 30x − 400 = 0
    4. x² − 20x − 400 = 0

    Answer: c) x² + 30x − 400 = 0

    Upstream time minus downstream time is 1 hour: 15/(20−x) − 15/(20+x) = 1. Clearing denominators gives 30x = 400 − x², or x² + 30x − 400 = 0.

  8. What is the‌ speed‌ of the current?
    1. 20 km/h
    2. 10 km/h
    3. 15 km/h
    4. 25 km/h

    Answer: b) 10 km/h

    Factorise x² + 30x − 400 = (x + 40)(x − 10). A speed cannot be negative, so the current is 10 km/h.

  9. If ½ is a root of the quadratic‌ equation​ x² − mx − 5/4 = 0, then the value of m is
    1. 2
    2. −2
    3. −3
    4. 3

    Answer: b) −2

    Substitute x = ½: ¼ − m/2 − 5/4 = 0, so −m/2 = 1 and m = −2.

  10. Find the nature of the roots for the‌ quadratic‌ equation x² − 3x + 11 = 0.
    1. No roots
    2. No real roots
    3. Two equal roots
    4. Two distinct real roots

    Answer: b) No real roots

    D = (−3)² − 4(1)(11) = 9 − 44 = −35. A negative discriminant means no real roots. Note the equation does have roots, just not real ones — which is why (a) is wrong.

  11. The values of​ k​ for which the quadratic equation 2x² − kx + k = 0 has equal roots are
    1. 8 and 2
    2. 0 and 2
    3. −8 and 0
    4. 0 and 8

    Answer: d) 0 and 8

    Equal roots need D = 0: k² − 4(2)(k) = k² − 8k = k(k − 8) = 0. So k = 0 or k = 8.

  12. Amit is designing a web page for a display on a screen whose size (diagonal) is 1000 pixels. The width of the screen is 800 pixels. Which of the following equations can‌ be‌ used to calculate the height (h) of the screen?
    1. h² + 200×1800 = 0
    2. h² − 200×1800 = 0
    3. h² − 200 = 0
    4. h² − 1800 = 0

    Answer: b) h² − 200×1800 = 0

    The diagonal, width and height satisfy h² = 1000² − 800² = 360000. Since 360000 = 200 × 1800, the equation is h² − 200×1800 = 0.

  13. The safe area of a web page is 40 pixels less than the width and 190 pixels less than the height of the display screen. Which expression represents the‌ safe​ area for a screen whose height is 200 pixels less than the screen width (w)?
    1. w² − 50w + 400
    2. w² − 350w + 30400
    3. w² − 430w + 15600
    4. w² − 200w + 7600

    Answer: c) w² − 430w + 15600

    Height is w − 200, so the safe area is (w − 40)(w − 200 − 190) = (w − 40)(w − 390) = w² − 430w + 15600.

Frequently asked questions

How many Quadratic Equations MCQs are there for Class 10 Maths?

This page has 13 multiple choice questions on Quadratic Equations, each with the correct answer and a worked explanation. Every question has been checked against the CBSE 2026-27 syllabus.

Which topics have been removed from Quadratic Equations in the 2026-27 syllabus?

The following are no longer assessed in 2026-27: Completing the square as a method of solution; Situational problems on equations reducible to quadratic equations. Questions on these carry no marks, so they are not included here.

Is Completing the square as a method of solution still in the Class 10 Maths syllabus?

No. Completing the square as a method of solution is not part of the CBSE 2026-27 Class 10 Maths syllabus for Quadratic Equations. Many question banks online still include it, but it carries no marks this session.

What does the 2026-27 syllabus cover in Quadratic Equations?

Standard form ax² + bx + c = 0, a ≠ 0; Solution by factorisation and by the quadratic formula — real roots only; Relationship between the discriminant and the nature of the roots; Situational problems based on quadratic equations. Every question on this page tests one of these.

How many marks is each Quadratic Equations MCQ worth?

Each objective question carries 1 mark in the CBSE Class 10 Maths paper. The practice set on this page keeps a running total as you answer, so you can see your score out of 13.

Quadratic Equations — chapter notes

A quadratic equation is any equation that can be written in the standard form ax² + bx + c = 0 with a ≠ 0. You have two solving methods: factorisation, which is fastest when the middle term splits neatly, and the quadratic formula, which always works. The discriminant b² − 4ac tells you what to expect before you solve — positive means two distinct real roots, zero means two equal roots, negative means no real roots. Questions asking for the value of k that gives equal roots are simply setting the discriminant to zero.

The word problems are where marks are won and lost: speed and time, upstream and downstream, areas and dimensions. Form the equation from the condition given, solve it, then check both roots against the situation and reject the one that makes no sense — a speed or a length cannot be negative. Stating that rejection explicitly is worth marks.