# CAT Quantitative Aptitude Questions | CAT Algebra - Linear Equations; Quadratic Equations

###### CAT Questions | Algebra | Quadratic Equations - Real roots

The question is about Real roots. Framing and solving equations is an integral part of Linear Equations and Quadratic Equations. Get as much practice as you can in these two topics because the benefits of being good at framing equations will be useful in other concepts. Note: If roots are real, then the discriminant is ≥ 0.

Question 16: If f(y) = x2 + (2p + 1)x + p2 - 1 and  x is a real number, for what values of ‘p' the function becomes 0?

1. p > 0
2. p > -1
3. p ≥ $$frac{-5}{4}\\$ 4. p ≤ $\frac{3}{4}\\$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from CAT Algebra - Quadratic Equations: If roots are real then the discriminant is ≥ 0. The function f$y) is a quadratic equation.
It is given that x is real.
So the discriminant of f(y) ≥ 0
i.e. D = b2 - 4ac ≥ 0 or
(2p + 1)2 – 4(p2 - 1) ≥ 0
4p2 + 4p + 1 – 4 (p2 - 1)  ≥ 0
4p + 5 ≥ 0
Or p ≥ $$frac{-5}{4}\\$ The question is "If f$y) = x2 + (2p + 1)x + p2 - 1 and  x is a real number, for what values of ‘p' the function becomes 0?"

##### Hence the answer is "p ≥ $$frac{-5}{4}\\$" Choice C is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Online Preparation | CAT Algebra Videos On YouTube #### Other useful sources for Algebra Questions | Linear Quadratic Sample Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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