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A polynomial with integer coefficients is of the form \(7x^4 + a_3 x^3 + a_2 x^2 + a_1 x - 14 = 0\). Find the number of different possible rational roots of this polynomial.

 May 21, 2019
 #1
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I might be simplifying this too much but there can only be a maximum of 4 becasue 4 is the degree.

Maybe there is less than 4

 May 21, 2019
edited by Melody  May 21, 2019
 #2
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+1

I don't think you umderstood the question. The guest is not asking for the maximal amount of rational roots the polynomial can have.

Guest May 21, 2019
 #3
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Yes ok   laugh

Melody  May 21, 2019
 #4
avatar+6046 
+2

any rational roots are a factor of the constant term divided by a factor of the coefficient of the highest degree term.

 

here the constant term is -14 with factors +/- 1, +/- 2, +/- 7 +/- 14

and the leading coefficient is 7 with factors +/- 1, +/- 7

 

thus we have possible rational roots

 

+/- 1/7

+/- 2/7

+/- 1

+/- 2

+/- 7

+/- 14

 

a total of 12 possible rational roots

Rom  May 21, 2019
edited by Rom  May 21, 2019
edited by Rom  May 21, 2019
 #5
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+2

Isn't 14 a factor of 14 too?

Guest May 21, 2019
 #6
avatar+6046 
+2

sigh, it sure is.  Add 14 and -14 to the list bringing it to 12 possible rational roots.

Rom  May 21, 2019
 #7
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0

Thanks Rom,

I didn't know that, I shall try and remember.   laugh

 

 

I mean I did not know this...

Any rational roots are a factor of the constant term divided by a factor of the coefficient of the highest degree term.

Melody  May 23, 2019
edited by Melody  May 23, 2019

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