Practice Questions on Quadratic Equations Last Updated : 23 Jul, 2025 Comments Improve Suggest changes Like Article Like Report Quadratic equations are everyday concepts with real-life applications. Understanding them is essential for solving aptitude and reasoning questions. This article offers a variety of easy-to-understand quadratic equations questions. Whether you’re a student or want to enhance your aptitude and reasoning skills, these questions and explanations will help you improve your problem-solving abilities.Table of ContentWhat is a Quadratic Equation? Related ArticlesImportant Formulas / ConceptsPractice Questions on Quadratic Equations : Solved Practice Questions on Quadratic Equations : Unsolved What is a Quadratic Equation? To define in simple words , quadratic equation is a 2nd-degree equation with syntax as ax2 + bx + c = 0 , where 'x' is an unknown variable a, b, and c's are constants (real numbers)and a is not equal to 0. To solve this kind of equation, you can use methods such as factoring, completing the square, or quadratic formula (also known as the Shree Dharacharya formula) . Each method helps find the values of x that satisfy the equation.Related Articles:Quadratic EquationsQuadratic FormulaRoots of Quadratic EquationImportant Formulas / ConceptsStandard Form of Quadratic Equation : ax2 + bx + c = 0 where 'x' is an unknown variable , 'a, b, and c' are constants (real numbers) and a is not equal to 0. Roots of Quadratic Equation Formula : x = [- b ± √(b2 – 4ac)]/2a and b2 - 4ac = D is called the Determinant of the quadratic equation.Range of quadratic expression : Maximum and Minimum value of y = ax2 + bx + c = 0 occurs at x = - (b/2a) irrespective of a < 0 or a > 0 respectively .Sum of Roots of Quadratic Equation : Sum of the roots α + β is equal to -b/a ( = - Coefficient of x / Coefficient of x2)Product of Roots of Quadratic Equation : Product of roots α . β is equal to c/a ( = Constant term / Coefficient of x2 )Difference of Roots of Quadratic Equation : Difference of roots α - β is equal to √D/a .Relation between roots and coefficient : (x - α) (x - β ) = 0 or x2 -(sum of roots) x + product of roots = 0.Practice Questions on Quadratic Equations : Solved 1. Solve the quadratic equation using factorization : x2 - 4x + 4 = 0.x2 - 4x + 4 = 0\Rightarrow x2- 2x - 2x + 4 = 0\Rightarrow x(x - 2) - 2 (x - 2) = 0\Rightarrow (x - 2)(x - 2) = 0\Rightarrow (x - 2)2 = 0Therefore x = 22. Form a quadratic equation with rational coefficients if one of its root is cot218°Given one of its root is cot218°Then , cot218° = (1 + cos 36° )/(1 - cos 36°) \Rightarrow (1 + (√5 + 1)/4)/(1 - (√5 + 1)/4) \Rightarrow 5 + 2√5Hence if α = 5 + 2√5 , β = 5 - 2√5Therefore , α + β = 10 ; α.β = 25 - 20 = 5So , the required quadratic equation will be x2 - 10x + 5 = 03. One root of mx2 - 10x + 3 = 0 is two third of the other root . Find the sum of the roots. α + 2α/3 = 10/m\Rightarrow 5α/3 = 10/m\Rightarrow α = 6/mand 2α/3 = 3/m\Rightarrow 2α2 = 9/m\Rightarrow 2.36/m2 = 9/m\Rightarrow m = 8Therefore , Sum = 10/ m = 10/8 = 5/4. 4. Form a quadratic equation with roots 2 and 3.Sum of roots = 2 + 3 = 5Product of roots = 2.3 = 6Therefore , quadratic equation is given by x2 + (sum of roots)x + (product of roots) = 0So , the required equation is x2 + 5x + 6 = 0.5. If x = 1 and x = 2 are solutions of the equation x3 + ax2+ bx + c = 0 and a + b = 1, then find the value b.a + b + c = -1 so, c = -2and 8 + 4a + 2b + c = 0\Rightarrow 4a + 2b = -6 \Rightarrow 2a + b = -3\Rightarrow a = -4 , b = 5Hence , a = -4, b = 5 and c = -2.6.Find the roots of the equation x4 + x3 - 19x2 - 49x - 30 = 0 , given that the roots are all rational numbers.Since all the roots are rational because , they are the divisors of -30.The divisors of -30 are 1, 2, 3, 4, 5, 6, 10, 15, 30 and -1,-2,-3,-4,-5,-6,-10,-15,-30.By remainder theorem , we find that -1,-2,-3 and 5 are the roots .Hence the roots are -1,-2,-3 and +5.Practice Questions on Quadratic Equations : Unsolved 1. Solve: 9 + 7x = 7x22. If one root is twice of the other , find the quadratic equation .3. Difference of roots is 2 and their sum is 7 , find the quadratic equation .4. One root of mx2 - 10x + 3 = 0 is two third of the other root . Find the product of the roots.5. If the product of the roots of the equation mx2 + 6x + 2m - 1 = 0 is -1 then find m .6. For what value of a , the difference of the roots of the equation (a - 2)x2 - (a - 4)x - 2 = 0 is equal to 3.7. For what value of a the sum of the roots of the equation x2 + 2(2 - a - a2)x - a2 = 0 is zero .8. The number of roots of the quadratic equation 8sec2x - 6secx + 1 = 0.9. If the roots of the equation 6x2 - 7x + k = 0 are rational , then find k.10. If x is real then find the maximum value of (3x2 + 9x + 17)/(3x2 + 9x + 7). Comment More infoAdvertise with us S sourabh_jain Follow Improve Article Tags : Mathematics Similar Reads Maths Mathematics, often referred to as "math" for short. It is the study of numbers, quantities, shapes, structures, patterns, and relationships. It is a fundamental subject that explores the logical reasoning and systematic approach to solving problems. 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A set is simply a collection of distinct elements, such as numbers, letters, or even everyday objects, that share a common property or rule.Example of SetsSome examples of sets include:A set of fruits: {apple, 3 min read PracticeNCERT Solutions for Class 8 to 12The NCERT Solutions are designed to help the students build a strong foundation and gain a better understanding of each and every question they attempt. This article provides updated NCERT Solutions for Classes 8 to 12 in all subjects for the new academic session 2023-24. The solutions are carefully 7 min read RD Sharma Class 8 Solutions for Maths: Chapter Wise PDFRD Sharma Class 8 Math is one of the best Mathematics book. It has thousands of questions on each topics organized for students to practice. RD Sharma Class 8 Solutions covers different types of questions with varying difficulty levels. The solutions provided by GeeksforGeeks help to practice the qu 5 min read RD Sharma Class 9 SolutionsRD Sharma Solutions for class 9 provides vast knowledge about the concepts through the chapter-wise solutions. These solutions help to solve problems of higher difficulty and to ensure students have a good practice of all types of questions that can be framed in the examination. Referring to the sol 10 min read RD Sharma Class 10 SolutionsRD Sharma Class 10 Solutions offer excellent reference material for students, enabling them to develop a firm understanding of the concepts covered. in each chapter of the textbook. As Class 10 mathematics is categorized into various crucial topics such as Algebra, Geometry, and Trigonometry, which 9 min read RD Sharma Class 11 Solutions for MathsRD Sharma Solutions for Class 11 covers different types of questions with varying difficulty levels. Practising these questions with solutions may ensure that students can do a good practice of all types of questions that can be framed in the examination. This ensures that they excel in their final 13 min read RD Sharma Class 12 Solutions for MathsRD Sharma Solutions for class 12 provide solutions to a wide range of questions with a varying difficulty level. With the help of numerous sums and examples, it helps the student to understand and clear the chapter thoroughly. Solving the given questions inside each chapter of RD Sharma will allow t 13 min read Like