Quadratic Equations Class 10 Worksheet – Complete Practice Guide
This Quadratic Equations Class 10 Online Practice Worksheet is designed for students who want structured, interactive practice for Chapter 4 of Class 10 Mathematics. It combines concept revision with instant answer checking so learners can practise independently on a phone, tablet or computer. The worksheet can create up to 2000 questions in a single test, while every generated question uses varied coefficients, forms and values to make repeated practice more useful.
What is a Quadratic Equation?
A quadratic equation in one variable is an equation of the form ax² + bx + c = 0, where a, b and c are real numbers and a ≠ 0. The highest power of the variable is two. The values of x that satisfy the equation are called its roots or zeros. Class 10 practice commonly includes equations that can be solved by factorisation, completing the square and the quadratic formula.
1. Solving by Factorisation
Factorisation is often the fastest method when an equation can be expressed as a product of two linear factors. For example, x² − 5x + 6 = 0 becomes (x − 2)(x − 3) = 0. Therefore x = 2 or x = 3. Always substitute the roots back into the original equation when checking your work.
2. Quadratic Formula
When factorisation is difficult, use the quadratic formula. For ax² + bx + c = 0, substitute the coefficients carefully and simplify the resulting expression.
The symbol ± means that two possible values can be obtained. If the discriminant is not a perfect square, the roots may be irrational. Students should simplify square roots and fractions rather than leaving an unnecessarily complicated expression.
3. Discriminant and Nature of Roots
The expression b² − 4ac is called the discriminant and is commonly represented by D. It gives information about the roots before solving the complete equation.
D > 0 → two distinct real roots
D = 0 → two equal real roots
D < 0 → no real roots
When D is positive and a perfect square, the roots are rational. When D is positive but not a perfect square, the roots are irrational. This classification is an important examination skill.
4. Relationship Between Roots and Coefficients
If α and β are the roots of ax² + bx + c = 0, then their sum and product are connected directly to the coefficients.
These relationships are useful when a question asks for the sum or product of roots, or asks you to construct an equation when the roots are known. If the roots are p and q, an equation with those roots can be written as x² − (p + q)x + pq = 0.
5. Word Problems and Applications
Quadratic equations can model problems involving consecutive integers, areas, dimensions, speeds and other quantities. Read the question carefully, define the unknown quantity, form the equation and reject values that do not make sense in the original situation. For example, a length or time normally cannot be negative even though algebra may produce a negative mathematical root.
6. How to Use This Online Worksheet
Choose the number of questions, question type, difficulty and timer. Select Start New Test before answering. Each question has its own answer box and Check Answer button. A correct response turns the answer area green and a wrong response turns it red. The answer is deliberately hidden until the question has been checked. After checking, the Show Answer button becomes available. Use Shuffle Whole Worksheet to generate a fresh arrangement and new values.
7. Smart Practice Strategy
Begin with Easy questions to establish accuracy, then move to Medium and Hard questions. Do not rely only on memorising the quadratic formula: practise recognising the standard form, identifying coefficients, calculating the discriminant, choosing a method and verifying roots. After each test, review the questions you missed and repeat the same topic with a different random set.
Exam Tips for Chapter 4
Write the equation in standard form before identifying a, b and c. Keep brackets around negative coefficients while substituting into formulas. Show enough working for factorisation and discriminant calculations. In word problems, state the final answer with its correct unit where applicable. Finally, check whether your roots satisfy the original equation.
Practice makes quadratic equations easier. Use this DigiSadhan worksheet regularly to improve speed, accuracy and confidence for Class 10 Mathematics examinations.