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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If 2 roots of an equation x^2-3x-3=0 are m and n, what is... tagged by: AAPL ##### This topic has 3 expert replies and 0 member replies ### Top Member ## If 2 roots of an equation x^2-3x-3=0 are m and n, what is... If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of m^2+n^2? A. 10 B. 12 C. 15 D. 24 E. 25 The OA is C. In this PS question I just need to find the roots and then solve the equation that is function of m and n, right? Can I find it using the second grade formula? Experts, can you give me any sugestion about how can I solve this PS question please? Thanks. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15385 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 Given xÂ² + bx + c = 0: -b = the SUM of the two roots. c = the PRODUCT of the two roots AAPL wrote: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of m^2+n^2? A. 10 B. 12 C. 15 D. 24 E. 25 In the equation above, b = -3 and c = -3. Thus: m+n = -b = -(-3) = 3. mn = c = -3. (m+n)Â² = mÂ² + nÂ² + 2mn. Substituting m+n = 3 and mn = -3 into (m+n)Â² = mÂ² + nÂ² + 2mn, we get: 3Â² = mÂ² + nÂ² + 2(-3) 9 = mÂ² + nÂ² - 6 15 = mÂ² + nÂ². The correct answer is C. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of m^2+n^2? A. 10 B. 12 C. 15 D. 24 E. 25 The OA is C. Hi AAPL, Let's take a look at your question. $$x^2-3x-3=0$$ For a quadratic equation, we know that, Sum of the roots = -b= -(-3) = 3 Product of the roots = c = -3 If roots of the given quadratic equation are m and n, then: $$m+n=3$$ $$mn=-3$$ Using the polynomial identity: $$\left(m+n\right)^2=m^2+n^2+2mn$$ Plugin in the known values in above equation. $$\left(3\right)^2=m^2+n^2+2\left(-3\right)$$ $$9=m^2+n^2-6$$ $$m^2+n^2=9+6$$ $$m^2+n^2=15$$ Therefore, Option C is correct. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 497 members Upvotes: 2867 GMAT Score: 800 Hi AAPL, We're told that the 2 roots of the equation x^2-3x-3=0 are M and N. We're asked for the value of M^2 + N^2. If you don't immediately recognize the Algebraic patterns involved, you can still use a bit of 'brute force' arithmetic (and the 'spread' of the answer choices) to get to the correct answer. To start, we know that there are 2 solutions - and the equation is relatively 'simple', so the solutions are likely 'close' to single-digit integers. We can do a few calculations to look for a pattern: IF... X = -2... X^2 - 3X - 3 = 7 X = -1... = 1 X = 0... = -3 X = 1... = -5 X = 2... = -5 X = 3... = -3 X = 4... = 1 Looking at this pattern, the 2 solutions will be (between -1 and 0, but closer to -1) and (between 3 and 4, but closer to 4). (-1)^2 + (4)^2 = 17. There's only one answer that's close to that.... Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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