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

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

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 ≥ $$frac{-5}{4}\\$ 4. p ≤ $\frac{3}{4}\\$ ## 2IIM : Best Online CAT Coaching #### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /-CAT Online Coaching ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2020Starts Sat, November 2nd, 2019 ### Explanatory Answer ##### Method of solving this CAT Question from CAT Algebra - Quadratic Equations: If roots are real then the discriminant is ≥ 0. The function f$y) is a quadratic equation.
It is given that x is real.
So the discriminant of f(y) ≥ 0
i.e. D = b2 - 4ac ≥ 0 or
(2p + 1)2 – 4(p2 - 1) ≥ 0
4p2 + 4p + 1 – 4 (p2 - 1)  ≥ 0
4p + 5 ≥ 0
Or p ≥ $$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. ###### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /- Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sat, Nov 2nd, 2019 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ##### 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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