Quadratic Equation CAT Questions 2025 PDF with Answers & Solutions

Overview: Struggling in Quadratic Equation CAT Questions? Fret not! We'll break down the basics in minutes and then equip you with valuable techniques like formula methods and factorization. We'll also share CAT-specific strategies to maximize your score.

What is CAT Exam 2025?

• The CAT, or Common Admission Test, is a crucial exam for students pursuing business and management careers at esteemed IIMs (Indian Institute of Management) and other top business schools in India.
• Acing the CAT offers access to IIMs and connects individuals to a strong alumni network, which can greatly boost career growth.
• Known for its difficulty, the CAT assesses an individual's aptitude and preparedness for admission to top-tier management programs.
• After the current examination cycle concludes, the CAT entrance exam 2024 notification will be announced.

In this blog, we will explore Quadratic Equation CAT Questions 2025 in depth including key concepts, types of problems asked, solving strategies, and tips to maximize your performance in this topic.

Read more: Logical Reasoning Questions for CAT with solutions

Download FREE Study Material for CAT Exam 2025 by SuperGrads

Read more: CAT Maths Syllabus 2025

Key Concepts Of Quadratic Equation CAT Questions 2025:

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 2025

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 2025

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

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 2025

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)

Explore: CAT 2025 Syllabus for MBA

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

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

Learn more: CAT Exam Day Guidelines

Tips To Solve Quadratic Equation CAT Questions 2025

Here are some tips for mastering quadratic equations to prepare for the CAT exam:

1. Master the Basics:
   - Ensure you are familiar with the CAT 2025 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 2025 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. 
   - Take mock tests featuring CAT quadratic equation questions to improve your exam temperament and time management skills.
   - Identify and work on your weaknesses by analyzing your performance in practice problems of CAT 2025 quadratic equation questions.

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.

Also Read: CAT Preparation Tips For Working Professional

Conclusion

You'll gain a valuable edge in the CAT quadratic equation 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. Remember, practice is key! Utilize the concepts and techniques discussed here by solving sample cat questions on quadratic equations and past CAT papers. With dedication in the CAT preparation and a solid understanding of quadratics, you'll be well on your way to conquering the CAT!

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