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

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New post 04 Feb 2019, 05:43
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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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Re: What is the number of the x-intercepts of y=x^4-3x^3+2x^2?  [#permalink]

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New post 04 Feb 2019, 06:35
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
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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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New post 04 Feb 2019, 14:40
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
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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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New post 06 Feb 2019, 08:13
=>

\(y = x^4-3x^3+2x^2\)
\(=> y = x^2(x^2-3x+2)\)
\(=> y = x^2(x-1)(z-2)\)
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
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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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New post 06 Feb 2019, 08:18
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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New post 06 Feb 2019, 08:54
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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, 08:54
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