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# What is the number of the x-intercepts of y=x^4-3x^3+2x^2?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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What is the number of the x-intercepts of y=x^4-3x^3+2x^2?  [#permalink]

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04 Feb 2019, 04:43
00:00

Difficulty:

25% (medium)

Question Stats:

63% (00:57) correct 37% (00:59) wrong based on 35 sessions

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[GMAT math practice question]

What is the number of the $$x$$-intercepts of $$y=x^4-3x^3+2x^2?$$

A. one
B. two
C. three
D. four
E. five

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Status: Manager Joined: 27 Oct 2018 Posts: 162 Location: Malaysia Concentration: Strategy, International Business GPA: 3.67 WE: Pharmaceuticals (Health Care) Re: What is the number of the x-intercepts of y=x^4-3x^3+2x^2? [#permalink] ### Show Tags 04 Feb 2019, 05:35 for x-intercepts to occur, y = 0. $$x^4-3x^3+2x^2 = 0$$ $$x^2(x^2-3x+2) = 0$$ $$x^2(x-2)(x-1) = 0$$ so possible roots for the equation are 0,2,1 C _________________ ...Thanks for KUDOS Senior Manager Joined: 17 Mar 2014 Posts: 439 Re: What is the number of the x-intercepts of y=x^4-3x^3+2x^2? [#permalink] ### Show Tags 04 Feb 2019, 13:40 MathRevolution wrote: [GMAT math practice question] What is the number of the $$x$$-intercepts of $$y=x^4-3x^3+2x^2?$$ A. one B. two C. three D. four E. five $$x$$-intercepts of $$y=x^4-3x^3+2x^2$$ means value of $$x$$ when $$y$$$$=0$$ So find out value $$x$$ when $$0=x^4-3x^3+2x^2?$$ $$x^4-3x^3+2x^2=0$$ $$x^2(x^2-3x+2)=0$$ $$x^2(x-2)(x-1)=0$$ x=0,1,2 SO answer should be C i.e. three Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6978 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the number of the x-intercepts of y=x^4-3x^3+2x^2? [#permalink] ### Show Tags 06 Feb 2019, 07:13 => $$y = x^4-3x^3+2x^2$$ $$=> y = x^2(x^2-3x+2)$$ $$=> y = x^2(x-1)(z-2)$$ The $$x$$-intercepts occur when $$y = 0$$. This occurs when $$x = 0, x = 1$$ and $$x = 2$$. There are three $$x$$-intercepts. Therefore, the answer is C. Answer: C _________________ 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$149 for 3 month Online Course"
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Re: What is the number of the x-intercepts of y=x^4-3x^3+2x^2?  [#permalink]

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06 Feb 2019, 07:18
HI Bunuel,

Please tag as Coordinate Geometry, not Functions and Custom Characters.
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Re: What is the number of the x-intercepts of y=x^4-3x^3+2x^2?  [#permalink]

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06 Feb 2019, 07:54
NandishSS wrote:
HI Bunuel,

Please tag as Coordinate Geometry, not Functions and Custom Characters.

_______________
Done. Thank you.
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Re: What is the number of the x-intercepts of y=x^4-3x^3+2x^2?   [#permalink] 06 Feb 2019, 07:54
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