# CAT 2022 Question Paper | Quant Slot 2

###### CAT Previous Year Paper | CAT Quant Questions | Question 9

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 9 : Let $r$ and $c$ be real numbers. If $r$ and $-r$ are roots of $5 x^3+c x^2-10 x+9=0$, then $c$ equals

1. $-$frac{9}{2}$ 2. $$frac{9}{2}$ 3. $-4$ 4. $4$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer Since r and$-r$ are the roots of the cubic equation $5 x ^ { 3 } + c x ^ { 2 } - 10 x + 9 = 0$
$5 ( r ) ^ { 3 } + c ( r ) ^ { 2 } - 10 ( r ) + 9 = 0$
$5 ( - r ) ^ { 3 } + c ( - r ) ^ { 2 } - 10 ( - r ) + 9 = 0$
$5 r ^ { 3 } + c r ^ { 2 } - 10 r + 9 = 0$
$- 5 r ^ { 3 } + c r ^ { 2 } + 10 r + 9 = 0$
10 r3 - 20 r = 0
r3 - 2r = 0
r (r2 - 2) = 0
r = $$pm $sqrt { 2 }$ Assuming the third root of the cubic equation as k, we can reconstruct it as… $$ x - $sqrt { 2 }$$ x + $sqrt { 2 } )$ x - k ) = 0$
$$left$ x ^ { 2 } - 2 $right)$ x - k ) = 0$
$x ^ { 3 } - k x ^ { 2 } - 2 x + 2 k = 0$
$5 x ^ { 3 } + c x ^ { 2 } - 10 x + 9 = 0$ can be re-written by making the coefficient of x3 as 1.
$x ^ { 3 } + $frac { c } { 5 } x ^ { 2 } - 2 x + $frac { 9 } { 5 } = 0$ $x ^ { 3 } + \frac { c } { 5 } x ^ { 2 } - 2 x + \frac { 9 } { 5 } = 0$ and $x ^ { 3 } - k x ^ { 2 } - 2 x + 2 k = 0$ are the same. $k = \frac { - c } { 5 }$ $2 k = \frac { 9 } { 5 }$ This implies, $c = \frac { - 9 } { 2 }$ The question is " Let $r$ and $c$ be real numbers. If $r$ and $-r$ are roots of $5 x^3+c x^2-10 x+9=0$, then $c$ equals " ##### Hence, the answer is '$-\frac{9}{2}$' Choice A is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Prepare for CAT 2024 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### 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! ##### 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? Mobile:$91$ 99626 48484 / 94459 38484
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