Class 10 Quadratic Equations Practice Questions
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CLASS 10 QUADRATIC EQUATIONS PRACTICE QUESTIONS
SECTION A — MCQs
The quadratic equation x² − 5x + 6 = 0 has:
A. no real roots
B. two equal real roots
C. two distinct real roots
D. one real rootThe value of the discriminant of the equation 2x² − 4x + 2 = 0 is:
A. 0
B. 4
C. −4
D. 8For which value of k does the equation x² + kx + 9 = 0 have equal roots?
A. 6
B. −6
C. 12
D. −12If the discriminant of a quadratic equation is negative, then the roots are:
A. real and equal
B. real and unequal
C. irrational
D. not realThe sum of the roots of the equation 3x² − 7x − 2 = 0 is:
A. 7/3
B. −7/3
C. 2/3
D. −2/3
SECTION B — 1-MARK QUESTIONS
Write the standard form of a quadratic equation.
Identify whether x² − 9 = 0 is a quadratic equation.
Find the value of the discriminant of x² + 4x + 4 = 0.
State the condition for a quadratic equation to have no real roots.
How many real solutions does the equation x² + 1 = 0 have?
SECTION C — 2-MARK QUESTIONS
Solve the quadratic equation x² − 7x + 10 = 0 by factorisation.
Find the roots of 2x² − 5x = 0.
Determine the nature of roots of the equation 4x² − 4x + 1 = 0.
Find the value of k for which the equation x² + kx + 16 = 0 has equal roots.
If the discriminant of a quadratic equation is 9, state the nature of its roots.
SECTION D – 3 MARK QUESTIONS
Solve the quadratic equation 3x² − 5x − 2 = 0 using quadratic formula.
Solve x² + 7x + 10 = 0 by factorisation.
Find the roots of 4x² − 7x + 3 = 0 and verify the result.
Find the value of k so that the quadratic equation x² + (k − 2)x + 1 = 0 has equal roots.
Determine the nature of roots of the equation 5x² − 3x + 7 = 0 without finding the roots.
SECTION E – 4 MARK QUESTIONS
Solve the quadratic equation 2x² − 7x + 3 = 0 using quadratic formula.
Find the roots of the equation x² − 8x + 12 = 0 and hence form the quadratic equation whose roots are increased by 2.
Solve the equation x² + 4x − 5 = 0 and verify the relationship between roots and coefficients.
Find the values of k for which the quadratic equation kx² − 4x + 1 = 0 has real and equal roots.
SECTION F – WORD PROBLEMS
Find two consecutive positive integers whose product is 132.
The sum of the squares of two consecutive natural numbers is 85. Find the numbers.
The length of a rectangular plot exceeds its breadth by 7 m and its area is 450 m². Find the dimensions of the plot.
A train travels a distance of 240 km at a certain speed. If the speed had been 8 km/h more, it would have taken 1 hour less. Find the original speed of the train.
The product of two positive numbers is 300 and their difference is 5. Find the numbers.
Class 10 Quadratic Equations Practice Questions – Complete CBSE Chapter Guide
Class 10 Quadratic Equations Practice Questions are one of the most searched resources by CBSE students because this chapter forms the backbone of algebra in Class 10 Mathematics. Quadratic Equations introduce students to equations of degree two and teach them how to solve real-life problems using algebraic methods. Regular practice with Class 10 Quadratic Equations Practice Questions is essential to develop accuracy, speed, and confidence for board examinations.
As per the latest CBSE blueprint, Quadratic Equations carry around 4–5 marks in the Class 10 Board Examination. Questions from this chapter are commonly asked as MCQs, 2–3 mark numerical problems, and 4-mark word problems. Since board questions are often application-based and slightly twisted, students must practise more than just basic NCERT questions.
Why Class 10 Quadratic Equations Practice Questions Are Very Important
Many students find Quadratic Equations challenging because they involve multiple solving techniques and interpretation of results. Class 10 Quadratic Equations Practice Questions help students:
Understand the standard form of a quadratic equation
Learn different methods of solving quadratic equations
Use the discriminant to determine the nature of roots
Solve real-life word problems accurately
Avoid common calculation and sign errors
This chapter is also closely linked with Polynomials, making it important to master both chapters together.
Topics Covered Through Class 10 Quadratic Equations Practice Questions
All Class 10 Quadratic Equations Practice Questions on this page are strictly aligned with the latest CBSE syllabus and include questions from the following topics:
Standard form of a quadratic equation
Solution of quadratic equations by:
Factorisation method
Quadratic formula
Nature of roots using the discriminant
Finding values of constants for given root conditions
Verification of solutions
Application-based word problems
No deleted or out-of-syllabus topics are included, ensuring focused and exam-relevant preparation.
Exam Pattern and Trends in Quadratic Equations
Recent CBSE board papers show that Class 10 Quadratic Equations Practice Questions are usually asked in the following formats:
MCQs based on discriminant and nature of roots
Short-answer questions solved by factorisation
Long-answer questions using quadratic formula
Word problems involving speed, area, numbers, and geometry
These questions often test conceptual understanding rather than memorisation, which is why consistent practice is crucial
How These Class 10 Quadratic Equations Practice Questions Help You Score 95+
Scoring high in Quadratic Equations requires clarity in concepts and systematic problem-solving. The Class 10 Quadratic Equations Practice Questions provided on this page are designed to:
Strengthen algebraic manipulation skills
Improve understanding of the discriminant
Help students choose the correct solving method
Prepare students for unfamiliar and tricky word problems
Reduce time spent on lengthy calculations in exams
With regular practice, students can turn this chapter into a high-scoring and confidence-boosting area.
Common Mistakes Students Make in Quadratic Equations
Students often lose marks due to avoidable mistakes such as:
Incorrect calculation of the discriminant
Wrong substitution of values in the quadratic formula
Choosing an unsuitable method of solution
Incomplete steps in long-answer questions
Errors in forming equations from word problems
Solving structured Class 10 Quadratic Equations Practice Questions regularly helps students overcome these errors naturally.
How to Use This Page Effectively
To get the best results from this page:
Start with MCQs to revise basic concepts
Practise 2-mark questions to build accuracy
Focus on 3- and 4-mark questions for board readiness
Spend extra time on word problems
Revise discriminant-based questions multiple times
Following this strategy ensures complete mastery of Class 10 Quadratic Equations Practice Questions before the board exam.
Who Should Use These Class 10 Quadratic Equations Practice Questions?
This page is ideal for:
CBSE Class 10 students
Students aiming for 95–99 marks in Mathematics
Teachers looking for exam-oriented practice material
Students revising for pre-boards and final exams
The questions are designed to match actual CBSE board difficulty levels.
Final Words
Quadratic Equations is one of the most important and scoring chapters in Class 10 Mathematics when practised properly. Regular practice using high-quality Class 10 Quadratic Equations Practice Questions ensures strong conceptual understanding and confidence during the exam.
This page is designed to act as a complete practice solution for mastering Quadratic Equations and achieving top scores in CBSE Class 10 Maths.