Quadratic Equation CAT Questions 2026 PDF (With Solutions)

Preparing for the CAT Exam 2026? Practise these Quadratic Equation CAT Questions to understand the topic better. This page covers important concepts, practice questions with step-by-step solutions, and a free PDF to help you revise roots, discriminants, equation formation, and other algebra problems.

Quadratic equations are an important part of CAT Quant. You may get direct questions from this topic or questions that combine it with other algebra concepts. Regular practice can help you solve them faster and avoid common mistakes in the CAT Exam.

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Key Takeaways

• Quadratic Equations are a frequently tested topic in CAT QA (Algebra section)
• Questions often test roots, nature of roots, and equation formation
• Can be solved using factorization or quadratic formula
• With practice, most questions can be solved in under 1 minute
• Strong fundamentals here improve performance in functions, inequalities, and polynomials

What are Quadratic Equation CAT Questions?

Quadratic equations are an important part of the Quantitative Ability section of the CAT Exam and are included in the Algebra topics covered under the CAT Syllabus. Questions from this topic test your understanding of concepts and your ability to solve problems within the given time.

we will explore the relevance of quadratic equations for CAT 2026, go through the fundamentals, provide useful tips and shortcuts, and finally, practice with sample CAT-level questions to strengthen your preparation.

Practice Now: Download CAT PYQ Quadratic Equations Question Bank

Key Concepts Of Quadratic Equation CAT Questions 2026

To solve a CAT quadratic equation questions, two common methods are utilized:

1. Standard Formula:

  Using the standard formula, any quadratic equation of the form ax^2 + bx + c = 0 can be solved quickly and efficiently using the following formula:

   x = (-b ± √(b^2 - 4ac)) / (2a)

Applying this formula means two solutions are obtained: one using the plus sign and the other using the minus sign. This method can be applied to any type of quadratic equation, whether or not it is factorable.

2. Factoring Method:

  This method involves factoring the quadratic expression to find its roots. It is a valuable technique for solving quadratic equations, especially when the equation is factorable.

Example: Consider the equation x² – 2x—6 = 0. Using the standard formula, we can solve this equation by finding the values of a, b, and c and then applying the formula to obtain the two solutions.

Original:

• x = -(-2) ± √(-2)^2 - 4(1)(-6) / 2(1)
• x = 2 ±√4 + 24/2
• x = 2 ± √28/2
• x = 2 ± 2√7/2
• x = 1 ± √7

Check: CAT Exam Pattern Section Wise

Important Quadratic Equation CAT Questions 2026

Q1. If α≠β but α²=5α−3 and β²=5β−3 then the equation whose roots are α/β and β/α.

1. 3x²−25x+3=03𝑥2−25𝑥+3=0
2. x²+5x−3=0𝑥2+5𝑥−3=0
3. x²−5x+3=0𝑥2−5𝑥+3=0
4. 3x2−19x+3=0

Answer: 3x2−19x+3=0

Q2. The number of real solutions of the equation x²−3|x|+2=0 is

1. 4
2. 1
3. 3
4. 2

Answer: 4

Q3. x² - 9x + |k| = 0 has real roots. How many integer values can 'k' take?

1. 40
2. 21
3. 20
4. 41

Answer: 41

Q4. Equation x² + 5x - 7 = 0 has roots a and b. The equation 2x² + px + q = 0 has roots a + 1 and b + 1. Find p + q.

1. 6
2. 0
3. -16
4. 2

Answer: -16

Read More: Important Geometry Questions for CAT 2026

Q5. Two numbers have an arithmetic mean of 9 and a geometric mean of 4. Then, these numbers are the roots of the quadratic equation x^2 + 18.

1. x²+18x−16=0
2. x²−18x+16=0
3. x²+18x+16=0
4. x²−18x−16=0

Answer: x²−18x+16=0

Q6. The given function is f(x) = x^2 + (2p + 1)x + p^2 - 1, where x is a real number. For what values of 'p' does the function equal 0 when p > 0?

1. p > 0
2. p > -1
3. p ≥ −5/4
4. p ≤ 34

Answer: p ≥ −5/4

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Q7. Suppose k is the largest integer such that the equation (x−1)²+2kx+11=0 has no real roots. Given that y is a positive real number, find the least possible value of (k/4y)+9y. 

1. 5
2. 6
3. 7
4. 8

Answer: 6

Practise: CAT Arithmetic Questions 2026

Q8. The number of integer solutions of the equation (x2−10)^{(x2−3x−10)}=1 is

1. 4
2. 5
3. 6
4. 8

Answer: 4

Q9. Given that both roots of the quadratic equation x2−2kx+k2+k−5=0 are less than 5, find the range of k.

1. (6,∞)
2. (5,6]
3. [ 4,5 ]
4. (−∞,4)

Answer: (−∞,4)

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Q10. Between the roots of the equation x^2+ax+1=0 is less than √5, the set of possible values of a is:

1. (3,∞)
2. (−∞,−3)
3. (−3,3)
4. (−3,∞)

Answer: (−3,3)

Q11. If 3x+2|y|+y=7 and x+|x|+3y=1, then x+2y𝑥+2𝑦 is

1. 0
2. 1
3. −43−43
4. 83

Answer: 0

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Q12. How many number of solutions the equation |x|(6x^2 + 1) = 5x^2 have?

1. 0
2. 8
3. 4
4. 5

Answer: 5

Q13. Two distinct roots of the equation 2x^2-6x+k=0 are α and β. Also (α+β) and αβ are the distinct roots of the equation x^2+px+p=0. Then, find the value of 8(k−p) is

1. 4
2. 5
3. 6
4. 0

Answer: 6

Tips To Solve Quadratic Equation CAT Questions 2026

To solve Quadratic Equation CAT Questions with confidence, start by understanding the basic formulas and methods. Practise different types of questions, solve CAT previous year papers, and review your mistakes. You can also use CAT online coaching to clear doubts and get more practice before the exam.

1. Master the Basics:

•   Ensure you are familiar with the CAT quadratic equation questions formula and understand how to use it.
•   Understand the relationship between cat questions on roots of quadratic equations and their coefficients.

2. Sharpen Your Problem-Solving Techniques:

•    Practice factoring CAT quadratic equation questions expressions as an alternative to using the quadratic formula.
•    Learn to identify the nature of roots based on the discriminant.

3. Develop a Strategic Approach:

•    Don't rely solely on the CAT quadratic equation questions formula; try factoring the equation first if possible.
•    Manage your time effectively as quadratic equation cat questions must be solved quickly.

4. Practice Makes Perfect:

•    Solve previous year CAT questions involving quadratic equations to familiarize yourself with question types and difficulty level. 
•    Identify and work on your weaknesses by analyzing your performance in practice problems of Quadratic equation CAT questions.
•  Take CAT Mock Tests featuring CAT quadratic equation questions to improve your exam temperament and time management skills.

5. Additional Tips:

•    Learn simplification tricks to save time.
•    Focus on accuracy rather than just speed.
•    Regularly review core concepts and formulas to keep them fresh in your mind.

By obeying these tips and practising consistently, you can upskill and build the confidence to effectively tackle quadratic equation questions in the CAT exam.

Quadratic equations differ from linear equations because quadratic equations contain an x^2 term, while linear equations do not. A term is considered quadratic when it has a degree of 2. Now let's delve deeper into the underlying concepts.

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Importance of Quadratic Equation CAT Questions in 2026

Quadratic Equation CAT Questions are a vital part of the Algebra section in the CAT Quantitative Aptitude paper. These questions test not only your mathematical understanding but also your logical thinking and speed. Here's why they hold such importance in your CAT preparation:

Frequent in CAT Papers: Quadratic Equation questions are regularly seen in the CAT exam. They may be asked directly or integrated into more complex algebra-based problems.

Strong Conceptual Foundation: Understanding quadratic equations builds a strong base for related algebraic topics such as:

• Polynomials
• Inequalities
• Functions
• Graph-based problems

High Accuracy Potential: These questions often follow predictable formats. If you know the standard methods like:

• Factoring
• Using the quadratic formula
• Completing the square you can attempt them with high accuracy.

Time-Saving Section: With practice, most quadratic problems can be solved in under a minute. This makes them great for saving time during the exam and focusing more on time-consuming questions later.

Application-Oriented Questions: In CAT, quadratic equations can also appear in word problems. You may need to find the correct roots, check whether a value fits the given conditions, or use the equation to solve a practical problem.

Read more: Complete CAT DILR Syllabus

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Conclusion

You'll gain a valuable edge in the Quadratic Equation CAT questions section by mastering cat questions on quadratic equations. This blog equips you with the knowledge and tools to solve these problems efficiently and accurately.

Keep practising quadratic equation questions and solve CAT previous year papers to get comfortable with different question types. Regular practice will help you understand the concepts better and avoid common mistakes in the CAT exam.