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# If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value  [#permalink]

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25 Jan 2019, 02:33
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25% (medium)

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[Math Revolution GMAT math practice question]

If $$2$$ roots of the equation $$x^2+px+q=0$$ are $$-3$$ and $$2$$, what is the value of $$p + q?$$

$$A. -5$$
$$B. -3$$
$$C. -1$$
$$D. 0$$
$$E. 1$$

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 09 Mar 2018 Posts: 997 Location: India Re: If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value [#permalink] ### Show Tags 25 Jan 2019, 03:01 1 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$2$$ roots of the equation $$x^2+px+q=0$$ are $$-3$$ and $$2$$, what is the value of $$p + q?$$ $$A. -5$$ $$B. -3$$ $$C. -1$$ $$D. 0$$ $$E. 1$$ When roots are given, i prefer the back solving approach (x+3) (x-2) x^2 + x -6 p+q = 1-6 = -5 A _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. GMAT Club Legend Joined: 18 Aug 2017 Posts: 4976 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value [#permalink] ### Show Tags 25 Jan 2019, 03:22 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$2$$ roots of the equation $$x^2+px+q=0$$ are $$-3$$ and $$2$$, what is the value of $$p + q?$$ $$A. -5$$ $$B. -3$$ $$C. -1$$ $$D. 0$$ $$E. 1$$ eqn would be x^2+x-6= 0 p=1 q=-6 p+q = 1-6; -5 IMO A _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value [#permalink] ### Show Tags 25 Jan 2019, 07:25 MathRevolution wrote: [Math Revolution GMAT math practice question] If the $$2$$ roots of the equation $$x^2+px+q=0$$ are $$-3$$ and $$2$$, where $$p$$ and $$q$$ are constants, what is the value of $$p + q?$$ $$A. -5$$ $$B. -3$$ $$C. -1$$ $$D. 0$$ $$E. 1$$ $$? = p + q$$ $$\left\{ \matrix{ \, - 1 = - 3 + 2 = {\rm{sum}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\, - p \hfill \cr \, - 6 = - 3 \cdot 2 = {\rm{product}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,q \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = p + q = 1 + \left( { - 6} \right) = - 5$$ $$\left( * \right)\,\,\,\left\{ \matrix{ a{x^2} + bx + c = 0\,\,,\,\,\,a \ne {\rm{0}} \hfill \cr \Delta \ge 0\,\,\,,\,\,\,{\rm{roots}}\,\,{x_1}\,\,{\rm{and}}\,\,{x_2} \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,{x_1} + {x_2} = - {b \over a} \hfill \cr \,{x_1} \cdot {x_2} = {c \over a} \hfill \cr} \right.$$ We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net CEO Joined: 12 Sep 2015 Posts: 3990 Location: Canada Re: If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value [#permalink] ### Show Tags 25 Jan 2019, 07:50 2 Top Contributor MathRevolution wrote: [Math Revolution GMAT math practice question] If $$2$$ roots of the equation $$x^2+px+q=0$$ are $$-3$$ and $$2$$, what is the value of $$p + q?$$ $$A. -5$$ $$B. -3$$ $$C. -1$$ $$D. 0$$ $$E. 1$$ GIVEN: the roots/solutions are x = -3 and x = 2 Notice that x = -3 and x = 2 are solutions to the equation (x + 3)(x - 2) = 0 If we expand and simplify the left side of the equation, we get: x² + x - 6 = 0 So, the equation x² + x - 6 = 0 has roots -3 and 2 Compare this to x² + px + q = 0 to see that p = 1 and q = -6 What is the value of p + q? p + q = 1 + (-6) = -5 Answer: A Cheers, Brent _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7999 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value [#permalink] ### Show Tags 27 Jan 2019, 18:28 => The equation of this form with roots $$-3$$ and $$2$$ is $$(x+3)(x-2) = 0$$ or $$x^2 + x – 6 = 0.$$ Thus, $$p = 1$$ and $$q = -6$$, and $$p + q = -5.$$ Therefore, the answer is A. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value   [#permalink] 27 Jan 2019, 18:28
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